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    <title>Pinboard (cshalizi)</title>
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    <description>recent bookmarks from cshalizi</description>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2211.15934"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/1605.08070"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2110.04338"/>
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  </channel><item rdf:about="https://link.springer.com/book/10.1007/978-3-031-97239-3">
    <title>Signature Methods in Finance: An Introduction with Computational Applications | Springer Nature Link</title>
    <dc:date>2026-06-13T04:04:14+00:00</dc:date>
    <link>https://link.springer.com/book/10.1007/978-3-031-97239-3</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This Open Access volume offers an accessible entry point into the fast-growing field of signature methods in finance. It is written for early-career researchers and quantitatively minded practitioners—quant analysts and applied researchers—seeking a clear, practical introduction. It highlights recent developments and includes coding examples to help readers apply signature methods in practice.
"The advantages of modeling financial markets from a path-wise perspective, rather than as a traditional series of returns, are increasingly gaining recognition. Signature methods provide a parsimonious description of paths of stochastic processes and, through the signature kernel, open a rich and compelling framework at the interface between machine learning and mathematical finance."]]></description>
<dc:subject>to:NB books:noted path_signatures time_series stochastic_processes finance kernel_methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a5cf1e7772a2/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:path_signatures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:finance"/>
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<item rdf:about="https://arxiv.org/abs/1910.09707">
    <title>[1910.09707] A Fresh Look at the &quot;Hot Hand&quot; Paradox</title>
    <dc:date>2026-02-20T15:30:29+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.09707</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We use the backward Kolmogorov equation approach to understand the apparently paradoxical feature that the mean waiting time to encounter distinct fixed-length sequences of heads and tails upon repeated fair coin flips can be different. For sequences of length 2, the mean time until the sequence HH (heads-heads) appears equals 6, while the waiting time for the sequence HT (heads-tails) equals 4. We give complete results for the waiting times of sequences of lengths 3, 4, and 5; the extension to longer sequences is straightforward (albeit more tedious). We also derive the moment generating functions, from which any moment of the mean waiting time for specific sequences can be found. Finally, we compute the mean waiting times T2nH for 2n heads in a row and Tn(HT) for n alternating heads and tails. For large n, T2nH∼3Tn(HT). Thus distinct sequences of coin flips of the same length can have very different mean waiting times."

!!!]]></description>
<dc:subject>probability stochastic_processes recurrence_times via:vaguery redner.sidney in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0cf75072433c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:recurrence_times"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:vaguery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:redner.sidney"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03530-w">
    <title>Martingale Properties of Entropy Production and a Generalized Work Theorem with Decoupled Forward and Backward Processes | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:26:18+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03530-w</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work theorems that uses tools from stochastic calculus instead of path-integration. We further strengthen the equality in work theorems by evaluating expectations conditioned on an arbitrary initial state value. These generalizations extend the applicability of work theorems and offer new interpretations of entropy production in stochastic systems. Lastly, we discuss the violation of work theorems in far-from-equilibrium systems."]]></description>
<dc:subject>to:NB stochastic_differential_equations martingales entropy non-equilibrium stochastic_processes statistical_mechanics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a9ed490380d6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03555-1">
    <title>Measure-Theoretic Time-Delay Embedding | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:25:12+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03555-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The celebrated Takens’ embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic and that observations are noise-free, limiting its applicability in real-world scenarios. Motivated by these limitations, we formulate a measure-theoretic generalization that adopts an Eulerian description of the dynamics and recasts the embedding as a pushforward map between spaces of probability measures. Our mathematical results leverage recent advances in optimal transport. Building on the proposed measure-theoretic time-delay embedding theory, we develop a computational procedure that aims to reconstruct the full state of a dynamical system from time-lagged partial observations, engineered with robustness to handle sparse and noisy data. We evaluate our measure-based approach across several numerical examples, ranging from the classic Lorenz-63 system to real-world applications such as NOAA sea surface temperature reconstruction and ERA5 wind field reconstruction."]]></description>
<dc:subject>to:NB to_read state-space_reconstruction dynamical_systems stochastic_processes re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ddcab3885772/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_reconstruction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03547-1">
    <title>Error Bounds in a Smooth Metric for Brownian Approximation of Dynamical Systems via Stein’s Method | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:24:23+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03547-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We adapt Stein’s method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of smooth test functions under a functional correlation decay bound. For systems with a sufficiently fast polynomial rate of correlation decay, the error bound is of order 
$O(N^{−1/2})$, under an additional condition on the linear growth of variance. Applications include a family of interval maps with neutral fixed points and unbounded derivatives, and two-dimensional dispersing Sinai billiards."]]></description>
<dc:subject>to:NB central_limit_theorem stochastic_processes dynamical_systems ergodic_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4134e9e7c64c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03552-4">
    <title>Gaussian concentration bounds for probabilistic cellular automata | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:23:09+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03552-4</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish the conservation of GCB and, in the high-noise regime, demonstrate that GCB holds for the unique stationary measure. Additionally, we prove the equivalence of GCB for the space-time measure and its spatial marginals in the case of contractive probabilistic cellular automata. Furthermore, we explore the relationship between (non)-uniqueness and GCB in the context of space-time Gibbs measures for PCA and illustrate these results with examples."]]></description>
<dc:subject>to:NB concentration_of_measure random_fields stochastic_processes cellular_automata chazottes.jean-rene</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9f0c1770e032/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:concentration_of_measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cellular_automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chazottes.jean-rene"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03537-3">
    <title>Large Deviation Principle for Slow-Fast Systems with Infinite-Dimensional Mixed Fractional Brownian Motion | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:22:29+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03537-3</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This work is concerned with the large deviation principle (LDP) for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H \in (1/2, 1)$. We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply Khasminskii’s averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components. Finally, the moderate deviation principle (MDP) for the slow-fast systems is established based on the proof of the proposed LDP."]]></description>
<dc:subject>to:NB dynamical_systems large_deviations stochastic_processes long-range_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:58caae221a90/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:long-range_dependence"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2211.15934">
    <title>[2211.15934] Causal identification for continuous-time stochastic processes</title>
    <dc:date>2025-12-18T04:10:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2211.15934</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data collection have yielded near continuous-time measurements, from e.g. physiological monitors, wearable digital devices, and environmental sensors. Statistical methodology for estimating the causal effect of a time-varying treatment, measured discretely in time, is well developed. But discrete-time methods like the g-formula, structural nested models, and marginal structural models do not generalize easily to continuous time, due to the entanglement of uncountably infinite variables. Moreover, researchers have shown that the choice of discretization time scale can seriously affect the quality of causal inferences about the effects of an intervention. In this paper, we establish causal identification results for continuous-time treatment-outcome relationships for general cadlag stochastic processes under continuous-time confounding, through orthogonalization and weighting. We use three concrete running examples to demonstrate the plausibility of our identification assumptions, as well as their connections to the discrete-time g methods literature."]]></description>
<dc:subject>causality stochastic_processes causal_inference martingales in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:96f77e1ff841/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/doi/10.1073/pnas.2411731121">
    <title>A local–global principle for nonequilibrium steady states | PNAS</title>
    <dc:date>2025-12-18T02:50:13+00:00</dc:date>
    <link>https://www.pnas.org/doi/10.1073/pnas.2411731121</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of configurations. For nonequilibrium systems, there is no such property for which an analogous principle holds, hence no common explanation of the diverse forms of self-organization they exhibit. However, a flurry of recent empirical results has shown that a local property of configurations called “rattling” predicts the steady states of some nonequilibrium systems, leading to claims of a far-reaching principle of nonequilibrium self-organization. But for which nonequilibrium systems is rattling accurate, and why? We develop a theory of rattling in terms of Markov processes that gives simple and precise answers to these key questions. Our results show that rattling predicts a broader class of nonequilibrium steady states than has been claimed and for different reasons than have been suggested. Its predictions hold to an extent determined by the relative variance of, and correlation between, the local and global “parts” of a steady state. We show how these quantities characterize the local-global relationships of various random walks on random graphs, spin-glass dynamics, and models of animal collective behavior. Surprisingly, we find that the core idea of rattling is so general as to apply to equilibrium and nonequilibrium systems alike."]]></description>
<dc:subject>to:NB non-equilibrium self-organization statistical_mechanics stochastic_processes markov_models randall.dana to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1730b51f604e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-organization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:randall.dana"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03528-4">
    <title>Irreversibility as Divergence from Equilibrium | Journal of Statistical Physics</title>
    <dc:date>2025-11-20T20:42:22+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03528-4</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The entropy production is commonly interpreted as measuring the distance from equilibrium. However, this explanation lacks a rigorous description due to the absence of a natural equilibrium measure. The present analysis formalizes this interpretation by expressing the entropy production of a Markov system as a divergence with respect to particular equilibrium dynamics. These equilibrium dynamics correspond to the closest reversible systems in the information-theoretic sense. This result yields novel links between nonequilibrium thermodynamics and information geometry."

]]></description>
<dc:subject>to:NB physics non-equilibrium information_geometry markov_models stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:996c6add6ce2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2508.21055">
    <title>[2508.21055] Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon</title>
    <dc:date>2025-09-02T02:49:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2508.21055</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their distance to equilibrium remains close to its maximal value for a while and suddenly drops to zero as the time parameter reaches a critical threshold. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to interacting particle systems. It is now believed to be universal among fast-mixing high-dimensional processes. Yet, current proofs are heavily model-dependent, and identifying the general conditions that trigger a cutoff remains one of the biggest challenges in the quantitative analysis of finite Markov chains. The purpose of these lecture notes is to provide a self-contained introduction to this fascinating question, and to describe its recently-uncovered relations with entropy, curvature and concentration."]]></description>
<dc:subject>to:NB to_read markov_models stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4b52c6b91f38/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/us/universitypress/subjects/physics/mathematical-methods/probability-theory-quantitative-scientists?format=HB&amp;WT.mc_id=NGV_IOC_BC_BK%253b_PHYS%253b_Probability%2BTheory%2Bfor%2BQuantitative%2BScientists_Jul25">
    <title>Probability Theory for Quantitative Scientists | Cambridge University Press &amp; Assessment</title>
    <dc:date>2025-08-16T23:02:29+00:00</dc:date>
    <link>https://www.cambridge.org/us/universitypress/subjects/physics/mathematical-methods/probability-theory-quantitative-scientists?format=HB&amp;WT.mc_id=NGV_IOC_BC_BK%253b_PHYS%253b_Probability%2BTheory%2Bfor%2BQuantitative%2BScientists_Jul25</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Based on the long-running Probability Theory course at the Sapienza University of Rome, this book offers a fresh and in-depth approach to probability and statistics, while remaining intuitive and accessible in style. The fundamentals of probability theory are elegantly presented, supported by numerous examples and illustrations, and modern applications are later introduced giving readers an appreciation of current research topics. The text covers distribution functions, statistical inference and data analysis, and more advanced methods including Markov chains and Poisson processes, widely used in dynamical systems and data science research. The concluding section, 'Entropy, Probability and Statistical Mechanics' unites key concepts from the text with the authors' impressive research experience, to provide a clear illustration of these powerful statistical tools in action. Ideal for students and researchers in the quantitative sciences this book provides an authoritative account of probability theory, written by leading researchers in the field."

--- If Diaconis calls your probability textbook "mind-blowing", the rest of us should at least check it out...]]></description>
<dc:subject>to:NB books:noted probability statistics stochastic_processes statistical_mechanics of_course_its_really_a_spin_glass</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:62d2299db5f4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:of_course_its_really_a_spin_glass"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2407.14781">
    <title>[2407.14781] Bernstein-von Mises theorems for time evolution equations</title>
    <dc:date>2025-07-28T14:19:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.14781</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider a class of infinite-dimensional dynamical systems driven by non-linear parabolic partial differential equations with initial condition θ modelled by a Gaussian process `prior' probability measure. Given discrete samples of the state of the system evolving in space-time, one obtains updated `posterior' measures on a function space containing all possible trajectories. We give a general set of conditions under which these non-Gaussian posterior distributions are approximated, in Wasserstein distance for the supremum-norm metric, by the law of a Gaussian random function. We demonstrate the applicability of our results to periodic non-linear reaction diffusion equations
\[
\frac{\partial}{\partial t} u - \nabla u = f(u)
\[
\[
u(0) = \theta
\]
where f is any smooth and compactly supported reaction function. In this case the limiting Gaussian measure can be characterised as the solution of a time-dependent Schrödinger equation with `rough' Gaussian initial conditions whose covariance operator we describe."]]></description>
<dc:subject>to:NB stochastic_processes dynamical_systems central_limit_theorem nickl.richard gaussian_processes bayesian_consistency</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4df4e0251977/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nickl.richard"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gaussian_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesian_consistency"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.00447">
    <title>[2107.00447] General Signature Kernels</title>
    <dc:date>2025-07-01T14:53:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.00447</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Suppose that γ and σ are two continuous bounded variation paths which take values in a finite-dimensional inner product space V. Recent papers have introduced the truncated and the untruncated signature kernel of γ and σ, and showed how these concepts can be used in classification and prediction tasks involving multivariate time series. In this paper, we introduce general signature kernels and show how they can be interpreted, in many examples, as an average of PDE solutions, and hence how they can be computed using suitable quadrature rules. We extend this analysis to derive closed-form formulae for expressions involving the expected (Stratonovich) signature of Brownian motion. In doing so, we articulate a novel connection between signature kernels and the hyperbolic development map, the latter of which has been a broadly useful tool in the analysis of the signature. As an application we evaluate the use of different general signature kernels as the basis for non-parametric goodness-of-fit tests to Wiener measure on path space."]]></description>
<dc:subject>to:NB path_signatures mathematics re:codename:catherine_wheel kernel_methods stochastic_processes goodness-of-fit via:mw-s have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a024ba063d90/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:path_signatures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:goodness-of-fit"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mw-s"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2405.00126">
    <title>[2405.00126] A variational approach to sampling in diffusion processes</title>
    <dc:date>2025-04-23T16:00:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2405.00126</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem in stochastic optimal control, so that the posterior density of the signal given the observation path could be sampled by adding a drift to the signal process. We show that this control-theoretic approach to sampling provides a common mechanism underlying several distinct problems involving diffusion processes, specifically importance sampling using Feynman-Kac averages, time reversal, and Schrödinger bridges."]]></description>
<dc:subject>to_read stochastic_processes stochastic_differential_equations control_theory_and_control_engineering information_theory raginsky.maxim via:mraginsky to_teach:statistics_and_generative_ai in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bb9efdd86c90/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:statistics_and_generative_ai"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1503.03585">
    <title>[1503.03585] Deep Unsupervised Learning using Nonequilibrium Thermodynamics</title>
    <dc:date>2025-04-10T18:40:59+00:00</dc:date>
    <link>https://arxiv.org/abs/1503.03585</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm."]]></description>
<dc:subject>density_estimation stochastic_processes generative_diffusion_models in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:053e927a1129/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:generative_diffusion_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2503.04020">
    <title>[2503.04020] An Approximate-Master-Equation Formulation of the Watts Threshold Model on Hypergraphs</title>
    <dc:date>2025-04-09T14:12:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2503.04020</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In traditional models of behavioral or opinion dynamics on social networks, researchers suppose that all interactions occur between pairs of individuals. However, in reality, social interactions also occur in groups of three or more individuals. A common way to incorporate such polyadic interactions is to study dynamical processes on hypergraphs. In a hypergraph, interactions can occur between any number of the individuals in a network. The Watts threshold model (WTM) is a well-known model of a simplistic social spreading process. Very recently, Chen et al. extended the WTM from dyadic networks (i.e., graphs) to polyadic networks (i.e., hypergraphs). In the present paper, we extend their discrete-time model to continuous time using approximate master equations (AMEs). By using AMEs, we are able to model the system with very high accuracy. We then reduce the high-dimensional AME system to a system of three coupled differential equations without any detectable loss of accuracy. This much lower-dimensional system is more computationally efficient to solve numerically and is also easier to interpret. We linearize the reduced AME system and calculate a cascade condition, which allows us to determine when a large spreading event occurs. We then apply our model to a social contact network of a French primary school and to a hypergraph of computer-science coauthorships. We find that the AME system is accurate in modelling the polyadic WTM on these empirical networks; however, we expect that future work that incorporates structural correlations between nearby nodes and groups into the model for the dynamics will lead to more accurate theory for real-world networks."]]></description>
<dc:subject>to:NB social_influence stochastic_processes networks porter.mason_a. re:do-institutions-evolve</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8a3aab250ab3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:social_influence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:porter.mason_a."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:do-institutions-evolve"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://maxim.ece.illinois.edu/teaching/spring23/SDE_book.pdf">
    <title>Stochastic Differential Equations: A Systems-Theoretic Approach</title>
    <dc:date>2025-04-02T11:54:05+00:00</dc:date>
    <link>https://maxim.ece.illinois.edu/teaching/spring23/SDE_book.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[--- Short draft book by MR, including a last chapter on generative diffusion models]]></description>
<dc:subject>stochastic_differential_equations control_theory_and_control_engineering stochastic_processes raginsky.maxim generative_diffusion_models downloaded books:noted in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:56a94e3cac83/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:generative_diffusion_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2501.16839">
    <title>[2501.16839] Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans</title>
    <dc:date>2025-02-03T00:35:34+00:00</dc:date>
    <link>https://arxiv.org/abs/2501.16839</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Among generative neural models, flow matching techniques stand out for their simple applicability and good scaling properties. Here, velocity fields of curves connecting a simple latent and a target distribution are learned. Then the corresponding ordinary differential equation can be used to sample from a target distribution, starting in samples from the latent one. This paper reviews from a mathematical point of view different techniques to learn the velocity fields of absolutely continuous curves in the Wasserstein geometry. We show how the velocity fields can be characterized and learned via i) transport plans (couplings) between latent and target distributions, ii) Markov kernels and iii) stochastic processes, where the latter two include the coupling approach, but are in general broader. Besides this main goal, we show how flow matching can be used for solving Bayesian inverse problems, where the definition of conditional Wasserstein distances plays a central role. Finally, we briefly address continuous normalizing flows and score matching techniques, which approach the learning of velocity fields of curves from other directions."]]></description>
<dc:subject>to:NB computational_statistics latent_variables stochastic_processes to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b41c5700d66a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:latent_variables"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://github.com/mxgmn/MarkovJunior">
    <title>GitHub - mxgmn/MarkovJunior: Probabilistic language based on pattern matching and constraint propagation, 153 examples</title>
    <dc:date>2024-12-11T15:38:33+00:00</dc:date>
    <link>https://github.com/mxgmn/MarkovJunior</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["MarkovJunior is a probabilistic programming language where programs are combinations of rewrite rules and inference is performed via constraint propagation."

--- Basically: Holland-esque production systems, it looks like.]]></description>
<dc:subject>programming probability stochastic_processes to_play_with_in_my_copious_free_time to:NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0afea063d1a4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_play_with_in_my_copious_free_time"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/book/10.1007/978-3-030-61871-1">
    <title>Foundations of Modern Probability | SpringerLink</title>
    <dc:date>2024-10-10T13:45:49+00:00</dc:date>
    <link>https://link.springer.com/book/10.1007/978-3-030-61871-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[--- WTH?  A new edition of Kallenberg from 3 years ago and I'm only discovering it now?
--- ETA: It's great.]]></description>
<dc:subject>to_read probability stochastic_processes re:almost_none downloaded books:owned books:recommended</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:44e800fda870/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:owned"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:recommended"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/BF02761077">
    <title>Guessing the next output of a stationary process (Ornstein, 1978) | Israel Journal of Mathematics</title>
    <dc:date>2024-09-16T19:15:55+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/BF02761077</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Suppose we start watching a stationary process at time 0. Then the conditional probability of a particular output at time -1, given the outputs at times 0 through $k$, will converge. In this paper we will show that we can make a guess, depending only on the outputs from 0 through $k$ (and not, of course, on the process) that will converge to the above limit with probability one."

--- WTH does the abstract reverse time?!?
--- The presentation in  Algoet [https://doi.org/10.1214/aop/1176989811] is actually much clearer, not that that's saying much.]]></description>
<dc:subject>in_NB prediction stochastic_processes ergodic_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b2a70a7b3907/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/journals/bernoulli/volume-25/issue-2/Towards-a-general-theory-for-nonlinear-locally-stationary-processes/10.3150/17-BEJ1011.full">
    <title>Towards a general theory for nonlinear locally stationary processes</title>
    <dc:date>2024-07-24T14:16:05+00:00</dc:date>
    <link>https://projecteuclid.org/journals/bernoulli/volume-25/issue-2/Towards-a-general-theory-for-nonlinear-locally-stationary-processes/10.3150/17-BEJ1011.full</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias expansions are proved for processes obeying an expansion in terms of the stationary approximation and derivative. In addition it is shown that this applies to some general nonlinear non-stationary Markov-models. In addition the results are applied to derive the asymptotic properties of maximum likelihood estimates of parameter curves in such models."]]></description>
<dc:subject>time_series stochastic_processes non-stationarity locally_stationary_processes in_NB re:random_features_for_locally-stationary_processes via:michael_w-s wu.wei-biao</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:45ac47a31da3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:locally_stationary_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:random_features_for_locally-stationary_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:michael_w-s"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wu.wei-biao"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2402.18477">
    <title>[2402.18477] Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes</title>
    <dc:date>2024-03-12T01:32:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.18477</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic differential equations (SDEs), which naturally imply causal relationships via "which variables enter the differential of which other variables". In this paper, we develop a kernel-based test of conditional independence (CI) on "path-space" -- solutions to SDEs -- by leveraging recent advances in signature kernels. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for loops) that leverage temporal information to recover the entire directed graph. Assuming faithfulness and a CI oracle, our algorithm is sound and complete. We empirically verify that our developed CI test in conjunction with the causal discovery algorithm reliably outperforms baselines across a range of settings."]]></description>
<dc:subject>to:NB causal_discovery dependence_measures stochastic_processes kernel_methods path_signatures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f65b2f6a9820/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dependence_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:path_signatures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2402.10157">
    <title>[2402.10157] Revisiting Stochastic Realization Theory using Functional Itô Calculus</title>
    <dc:date>2024-02-16T05:02:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.10157</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper considers the problem of constructing finite-dimensional state space realizations for stochastic processes that can be represented as the outputs of a certain type of a causal system driven by a continuous semimartingale input process. The main assumption is that the output process is infinitely differentiable, where the notion of differentiability comes from the functional Itô calculus introduced by Dupire as a causal (nonanticipative) counterpart to Malliavin's stochastic calculus of variations. The proposed approach builds on the ideas of Hijab, who had considered the case of processes driven by a Brownian motion, and makes contact with the realization theory of deterministic systems based on formal power series and Chen-Fliess functional expansions."]]></description>
<dc:subject>to:NB stochastic_processes stochastic_differential_equations raginsky.maxim</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:60c0f9933b6d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2212.13628">
    <title>[2212.13628] Functional Expansions</title>
    <dc:date>2023-12-08T19:03:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2212.13628</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often infinite-dimensional, thus challenging from a conceptual and computational perspective. In this work, we shed light on expansions of functionals. First, we treat static expansions made around paths of fixed length and propose a generalization of the Wiener series−the intrinsic value expansion (IVE). In the dynamic case, we revisit the functional Taylor expansion (FTE). The latter connects the functional Itô calculus with the signature to quantify the effect in a functional when a "perturbation" path is concatenated with the source path. In particular, the FTE elegantly separates the functional from future trajectories. The notions of real analyticity and radius of convergence are also extended to the path space. We discuss other dynamic expansions arising from Hilbert projections and the Wiener chaos, and finally show financial applications of the FTE to the pricing and hedging of exotic contingent claims."]]></description>
<dc:subject>to:NB stochastic_processes finance</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2ca680d2c220/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:finance"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://doi.org/10.1214/aoms/1177706638">
    <title>An Elementary Theorem Concerning Stationary Ergodic Processes on JSTOR</title>
    <dc:date>2023-12-02T02:39:26+00:00</dc:date>
    <link>https://doi.org/10.1214/aoms/1177706638</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[--- Cute.]]></description>
<dc:subject>stochastic_processes ergodic_theory have_read breiman.leo re:almost_none in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9b790bfccaaa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:breiman.leo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.07514">
    <title>[2206.07514] Networks of reinforced stochastic processes: a complete description of the first-order asymptotics</title>
    <dc:date>2023-06-28T16:17:48+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.07514</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization, which could be roughly defined as the almost sure long-run uniformization of the behavior of interacting processes. Specifically, we detect a regime of complete synchronization, where all the processes converge toward the same random variable, a second regime where the system almost surely converges, but there exists no form of almost sure asymptotic synchronization, and another regime where the system does not converge with a strictly positive probability. In this latter case, partitioning the system in cyclic classes according to the period of the interaction matrix, we have an almost sure asymptotic synchronization within the cyclic classes, and, with a strictly positive probability, an asymptotic periodic behavior of these classes."]]></description>
<dc:subject>stochastic_processes networks in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:64ecdf9574da/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/chapter/10.1007/978-3-662-08546-2_12">
    <title>Stochastic Realization Theory | SpringerLink</title>
    <dc:date>2023-05-19T03:28:05+00:00</dc:date>
    <link>https://link.springer.com/chapter/10.1007/978-3-662-08546-2_12</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The use of state-space models for modelling and processing of random signals was introduced by Kalman at the very beginning of the history of System Theory. Although spectacular successes have emerged from the introduction of these models (Kalman filtering to name just one), until quite recently there has not been any serious effort of putting together in a logically consistent way a theory of modelling and model representation in the stochastic frame. Expanding applications to diverse fields like Econometrics etc. and a multitude of nonstandard estimation problems arising in engineering applications seem now to render the need for such a theory more urgent."]]></description>
<dc:subject>to:NB stochastic_processes modeling via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:841a466f6d2f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:modeling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2304.11082">
    <title>[2304.11082] Fundamental Limitations of Alignment in Large Language Models</title>
    <dc:date>2023-05-02T19:41:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2304.11082</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["An important aspect in developing language models that interact with humans is aligning their behavior to be useful and unharmful for their human users. This is usually achieved by tuning the model in a way that enhances desired behaviors and inhibits undesired ones, a process referred to as alignment. In this paper, we propose a theoretical approach called Behavior Expectation Bounds (BEB) which allows us to formally investigate several inherent characteristics and limitations of alignment in large language models. Importantly, we prove that for any behavior that has a finite probability of being exhibited by the model, there exist prompts that can trigger the model into outputting this behavior, with probability that increases with the length of the prompt. This implies that any alignment process that attenuates undesired behavior but does not remove it altogether, is not safe against adversarial prompting attacks. Furthermore, our framework hints at the mechanism by which leading alignment approaches such as reinforcement learning from human feedback increase the LLM's proneness to being prompted into the undesired behaviors. Moreover, we include the notion of personas in our BEB framework, and find that behaviors which are generally very unlikely to be exhibited by the model can be brought to the front by prompting the model to behave as specific persona. This theoretical result is being experimentally demonstrated in large scale by the so called contemporary "chatGPT jailbreaks", where adversarial users trick the LLM into breaking its alignment guardrails by triggering it into acting as a malicious persona. Our results expose fundamental limitations in alignment of LLMs and bring to the forefront the need to devise reliable mechanisms for ensuring AI safety."

--- To over-simplify, suppose there's a bad region of the state space for the sequence-generating model, where it produces undesirable symbol strings.  (Bigoted, inaccurate, prejudicial to the stock price, uses four spaces for indenting code instead of tabs, whatever.)  If that region isn't shrunk all the way to zero, there's _some_ prompt, some sequence of symbols, which will kick the stochastic process into the bad region.  If the bad region is, in a Kullback-Leibler sense, well-separated from the good regions, the process can stay in bad places for quite a while.  (Paths out of the bad region are few and/or difficult.)  This is all done at a very high level of generality, where the details of neural networks, etc., are all completely abstracted away from, leaving just a stochastic process.]]></description>
<dc:subject>in_NB large_language_models_(so_called) have_read stochastic_processes re:large_language_models_in_statistical_perspective</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0b7cc7c67740/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_language_models_(so_called)"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:large_language_models_in_statistical_perspective"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.55.5050">
    <title>Phys. Rev. E 55, 5050 (1997) - Characterizing the dynamics of stochastic bistable systems by measures of complexity</title>
    <dc:date>2023-04-24T22:05:40+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.55.5050</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In the case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity or the mean escape time, respectively. For the problem of a fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows us to describe the structures of motion in more detail. Most complexity measures indicate the value of the correlation time at which the phenomenon of resonant activation occurs with an extremum."]]></description>
<dc:subject>have_read complexity_measures stochastic_processes kurths.jurgen cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 re:dissertation metastability in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ee4a2bd3bebb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:complexity_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kurths.jurgen"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:dissertation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:metastability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.67.041105">
    <title>Phys. Rev. E 67, 041105 (2003) - Influence of spatiotemporally correlated noise on structure formation in excitable media</title>
    <dc:date>2023-04-24T21:45:18+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.67.041105</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We discuss the influence of additive, spatiotemporally correlated (i.e., colored) noise on pattern formation in a two-dimensional network of excitable systems. The signature of spatiotemporal stochastic resonance (STSR) is analyzed using cross-correlation and information theoretic measures. It is found that the STSR behavior is affected by both the spatial and temporal correlations of the noise due to an interplay with the length scales of the deterministic network. Increasing the spatiotemporal noise correlation shifts the occurrence of STSR to smaller values of the noise variance. Additionally, if the spatial correlation of the noise exceeds that of the network, the excitation patterns disappear in favor of cloudy structures, directly rendering the underlying spatial noise field."]]></description>
<dc:subject>stochastic_processes spatio-temporal_statistics excitable_media stochastic_resonance have_read cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 pattern_formation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:160399963bae/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:excitable_media"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_resonance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:pattern_formation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2303.08992">
    <title>[2303.08992] Law of large numbers and central limit theorem for ergodic quantum processes</title>
    <dc:date>2023-04-22T13:55:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2303.08992</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise. Such ergodic quantum processes generalize independent quantum processes. An ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit."

--- Last tag means "mention in further reading, if this checks out".]]></description>
<dc:subject>stochastic_processes quantum_mechanics ergodic_theory mixing central_limit_theorem re:almost_none in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0ab8f9922f41/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:quantum_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/chapter/10.1007/bfb0008474">
    <title>Stochastic realization problems | SpringerLink</title>
    <dc:date>2023-03-27T15:07:23+00:00</dc:date>
    <link>https://link.springer.com/chapter/10.1007/bfb0008474</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The stochastic realization problem asks for the existence and the classification of all stochastic systems for which the output process equals a given process in distribution or almost surely. This is a fundamental problem of system and control theory. The stochastic realization problem is of importance to modelling by stochastic systems in engineering, biology, economics etc. Several stochastic systems are mentioned for which the solution of the stochastic realization problem may be useful. As an example recent research on the stochastic realization problem for the Gaussian factor model and a Gaussian factor system is discussed."]]></description>
<dc:subject>to:NB stochastic_processes re:AoS_project re:almost_none via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f2eb81ce173e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://npg.copernicus.org/articles/30/85/2023/">
    <title>NPG - Rain process models and convergence to point processes</title>
    <dc:date>2023-03-18T13:53:37+00:00</dc:date>
    <link>https://npg.copernicus.org/articles/30/85/2023/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A variety of stochastic models have been used to describe time series of precipitation or rainfall. Since many of these stochastic models are simplistic, it is desirable to develop connections between the stochastic models and the underlying physics of rain. Here, convergence results are presented for such a connection between two stochastic models: (i) a stochastic moisture process as a physics-based description of atmospheric moisture evolution and (ii) a point process for rainfall time series as spike trains. The moisture process has dynamics that switch after the moisture hits a threshold, which represents the onset of rainfall and thereby gives rise to an associated rainfall process. This rainfall process is characterized by its random holding times for dry and wet periods. On average, the holding times for the wet periods are much shorter than the dry ones, and, in the limit of short wet periods, the rainfall process converges to a point process that is a spike train. Also, in the limit, the underlying moisture process becomes a threshold model with a teleporting boundary condition. To establish these limits and connections, formal asymptotic convergence is shown using the Fokker–Planck equation, which provides some intuitive understanding. Also, rigorous convergence is proved in mean square with respect to continuous functions of the moisture process and convergence in mean square with respect to generalized functions of the rain process."]]></description>
<dc:subject>to:NB meteorology point_processes stochastic_processes convergence_of_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:08bc66b19a4f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:meteorology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:point_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convergence_of_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.03582">
    <title>[2109.03582] Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes</title>
    <dc:date>2023-02-15T19:57:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.03582</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time. By conditioning the process on its filtration, we introduce a family of higher order kernel mean embeddings (KMEs) that generalizes the notion of KME and captures additional information related to the filtration. We derive empirical estimators for the associated higher order maximum mean discrepancies (MMDs) and prove consistency. We then construct a filtration-sensitive kernel two-sample test able to pick up information that gets missed by the standard MMD test. In addition, leveraging our higher order MMDs we construct a family of universal kernels on stochastic processes that allows to solve real-world calibration and optimal stopping problems in quantitative finance (such as the pricing of American options) via classical kernel-based regression methods. Finally, adapting existing tests for conditional independence to the case of stochastic processes, we design a causal-discovery algorithm to recover the causal graph of structural dependencies among interacting bodies solely from observations of their multidimensional trajectories."

--- ETA after reading: This feels like a strange paper.  I'm not sure I truly understand what theiur "signature statistics" do, nor do I quite get the claimed advantage of higher-order process kernels over "first-order" kernels.  (Proofs are referred to other, older papers.)  And the notion of "causality" between processes seems very weird, since I don't see how it accounts for the flow of time, and of influence, within or across processes, they're being treated like big but indecomposable objects.  Probably should track down references and see if this makes more sense when I put those together.]]></description>
<dc:subject>to:NB stochastic_processes kernel_methods causal_discovery time_series statistical_inference_for_stochastic_processes hilbert_space re:codename:catherine_wheel two-sample_tests statistics have_read path_signatures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:105636bb7bad/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:two-sample_tests"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:path_signatures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2212.12839">
    <title>[2212.12839] Escape times for subgraph detection and graph partitioning</title>
    <dc:date>2023-01-18T03:12:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2212.12839</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We provide a rearrangement based algorithm for fast detection of subgraphs of k vertices with long escape times for directed or undirected networks. Complementing other notions of densest subgraphs and graph cuts, our method is based on the mean hitting time required for a random walker to leave a designated set and hit the complement. We provide a new relaxation of this notion of hitting time on a given subgraph and use that relaxation to construct a fast subgraph detection algorithm and a generalization to K-partitioning schemes. Using a modification of the subgraph detector on each component, we propose a graph partitioner that identifies regions where random walks live for comparably large times. Importantly, our method implicitly respects the directed nature of the data for directed graphs while also being applicable to undirected graphs. We apply the partitioning method for community detection to a large class of model and real-world data sets."]]></description>
<dc:subject>to:NB networks network_data_analysis community_discovery stochastic_processes mucha.peter</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f14fb18e0235/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:community_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mucha.peter"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2202.00666">
    <title>[2202.00666] Locally Typical Sampling</title>
    <dc:date>2023-01-17T02:27:30+00:00</dc:date>
    <link>https://arxiv.org/abs/2202.00666</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the language generation community for the last few years. In this work, we posit that the abstraction of natural language generation as a discrete stochastic process--which allows for an information-theoretic analysis--can provide new insights into the behavior of probabilistic language generators, e.g., why high-probability texts can be dull or repetitive. Humans use language as a means of communicating information, aiming to do so in a simultaneously efficient and error-minimizing manner; in fact, psycholinguistics research suggests humans choose each word in a string with this subconscious goal in mind. We formally define the set of strings that meet this criterion: those for which each word has an information content close to the expected information content, i.e., the conditional entropy of our model. We then propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models, which we call locally typical sampling. Automatic and human evaluations show that, in comparison to nucleus and top-k sampling, locally typical sampling offers competitive performance (in both abstractive summarization and story generation) in terms of quality while consistently reducing degenerate repetitions."]]></description>
<dc:subject>natural_language_processing stochastic_processes to_read information_theory in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:236279d2f53c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:natural_language_processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://hdsr.mitpress.mit.edu/pub/qixx99zn/release/1">
    <title>On Learnability Under General Stochastic Processes · Issue 4.4, Fall 2022</title>
    <dc:date>2022-12-09T20:08:14+00:00</dc:date>
    <link>https://hdsr.mitpress.mit.edu/pub/qixx99zn/release/1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Statistical learning theory under independent and identically distributed (iid) sampling and online learning theory for worst case individual sequences are two of the best developed branches of learning theory. Statistical learning under general non-iid stochastic processes is less mature. We provide two natural notions of learnability of a function class under a general stochastic process. We show that both notions are in fact equivalent to online learnability. Our results hold for both binary classification and regression."

--- Ungated: [https://arxiv.org/abs/2005.07605]]]></description>
<dc:subject>to:NB learning_theory online_learning low-regret_learning to_read tewari.ambuj learning_under_dependence dawid.a._philip stochastic_processes to_teach:childs_garden_of_statistical_learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d8309e159972/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:online_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-regret_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:tewari.ambuj"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dawid.a._philip"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.10698v1">
    <title>[2209.10698v1] Stochastic approach to study the properties of the complex patterns observed in cytokine and T-cells interaction process</title>
    <dc:date>2022-12-09T20:07:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.10698v1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Patterns in complex systems store hidden information of the system which is needed to be explored. We present a simple model of cytokine and T-cells interaction and studied the model within stochastic framework by constructing Master equation of the system and solving it. The solved probability distribution function of the model show classical Poisson pattern in the large population limit $M,Z\rightarrow large$ indicating the system has the tendency to attract a large number small-scale random processes of the cytokine population towards the basin of attraction of the system by segregating from nonrandom processes. Further, in the large $\langle Z\rangle$ limit, the pattern transform to classical Normal pattern, where, uncorrelated small-scale fluctuations are wiped out to form a regular but memoryless spatiotemporal aggregated pattern. The estimated noise using Fano factor shows clearly that the cytokine dynamics is noise induced process driving the system far away from equilibrium."

--- Can't remember what led me to open this tab back in September.  Maybe a teaching example?!?]]></description>
<dc:subject>to:NB immunology stochastic_processes via:???</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c1e8002b03b9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:immunology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:???"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/BF01448198">
    <title>Stochastic control and nonequilibrium thermodynamical systems | SpringerLink</title>
    <dc:date>2022-06-28T14:14:45+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/BF01448198</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Minus the logarithm of the density of a diffusion process is shown to be the value function of a stochastic control problem, where the controlled equation evolves backward in time. For nonequilibrium thermodynamical systems, this provides a Hamilton-Jacobi-like theory, where the action is a local entropy function. This variational principle may also be seen as a rigorous version of the formal Onsager-Machlup principle. For the Ornstein-Uhlenbeck model of physical Brownian motion, the principle is related to a pathwise Newton law. For the latter model, several other pathwise results are derived, which strengthen the classical thermodynamical results on the averages. In particular, the (stochastic) Helmholtz free energy is shown to be a backward submartingale with respect to the natural filtration."

--- Probably via:ded-maxim but the tab's been open so long...]]></description>
<dc:subject>non-equilibrium thermodynamics large_deviations control_theory_and_control_engineering via:? stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5fe4eb5a9c77/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:thermodynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:?"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2111.12603">
    <title>[2111.12603] Strong Invariance Principles for Ergodic Markov Processes</title>
    <dc:date>2022-06-19T17:05:18+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.12603</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have been limited. In this paper, we obtain strong invariance principles for a broad class of ergodic Markov processes. Strong invariance principles provide a unified framework for analysing commonly used estimators of the asymptotic variance in settings with a dependence structure. We demonstrate how this can be used to analyse the batch means method for simulation output of Piecewise Deterministic Monte Carlo samplers. We also derive a fluctuation result for additive functionals of ergodic diffusions using our strong approximation results."]]></description>
<dc:subject>central_limit_theorem stochastic_processes convergence_of_stochastic_processes markov_models re:almost_none in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:23ae04823e1b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convergence_of_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.research-collection.ethz.ch/handle/20.500.11850/354751">
    <title>Dynamic Coarse-Graining via Large-Deviation Theory - Research Collection</title>
    <dc:date>2022-06-12T06:11:55+00:00</dc:date>
    <link>https://www.research-collection.ethz.ch/handle/20.500.11850/354751</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistical_mechanics non-equilibrium large_deviations stochastic_processes markov_models have_skimmed in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:47e2725ff00f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://iopscience.iop.org/article/10.1088/1751-8121/aa669a">
    <title>WKB theory of large deviations in stochastic populations - IOPscience</title>
    <dc:date>2022-06-12T05:52:36+00:00</dc:date>
    <link>https://iopscience.iop.org/article/10.1088/1751-8121/aa669a</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics—such as those determining population extinction, fixation or switching between different states—are presently in a focus of attention of statistical physicists. We review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation allows one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and multiple, but also briefly consider populations on heterogeneous networks and spatial populations. The spatial setting also allows one to study large fluctuations of the speed of biological invasions. Finally, we briefly discuss possible directions of future work."

--- Ungated: [https://arxiv.org/abs/1612.01470]]]></description>
<dc:subject>stochastic_processes large_deviations re:do-institutions-evolve have_skimmed in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9cb444d6d801/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:do-institutions-evolve"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/core/journals/journal-of-applied-probability/article/abs/an-ergodic-theorem-for-the-weighted-ensemble-method/C032C0720A9295B562CCEC138AB147CB">
    <title>An ergodic theorem for the weighted ensemble method | Journal of Applied Probability | Cambridge Core</title>
    <dc:date>2022-06-11T04:48:33+00:00</dc:date>
    <link>https://www.cambridge.org/core/journals/journal-of-applied-probability/article/abs/an-ergodic-theorem-for-the-weighted-ensemble-method/C032C0720A9295B562CCEC138AB147CB</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study weighted ensemble, an interacting particle method for sampling distributions of Markov chains that has been used in computational chemistry since the 1990s. Many important applications of weighted ensemble require the computation of long time averages. We establish the consistency of weighted ensemble in this setting by proving an ergodic theorem for time averages. As part of the proof, we derive explicit variance formulas that could be useful for optimizing the method."]]></description>
<dc:subject>to:NB particle_filters ergodic_theory stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e1d15f6d312a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.13615">
    <title>[2205.13615] Limit distributions of branching Markov chains</title>
    <dc:date>2022-06-10T14:07:30+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.13615</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study branching Markov chains on a countable state space (space of types) 𝒳, with the focus on the qualitative aspects of the limit behaviour of the evolving empirical population distributions. No conditions are imposed on the multitype offspring distributions at the points of 𝒳 other than to have the same average and to satisfy a uniform LlogL moment condition. We show that the arising population martingale is uniformly integrable. Convergence of population averages of the branching chain is then put in connection with stationary spaces of the associated ordinary Markov chain on 𝒳 (assumed to be irreducible and transient). This is applied, in particular, to the boundaries of appropriate compactifications of 𝒳. Final considerations consider the general interplay between the measure theoretic boundaries of the branching chain and the associated ordinary chain."

--- Assuming equal-expectation offspring distributions seems a little un-interesting but I should look.]]></description>
<dc:subject>branching_processes markov_models stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0d1c60549638/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:branching_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.04468">
    <title>[2206.04468] Bounded Rationality and Animal Spirits: A Fluctuation-Response Approach to Slutsky Matrices</title>
    <dc:date>2022-06-10T14:05:38+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.04468</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Slutsky equation, central in consumer choice theory, is derived from the usual hypotheses underlying most standard models in Economics, such as full rationality, homogeneity, and absence of interactions. We present a statistical physics framework that allows us to relax such assumptions. We first derive a general fluctuation-response formula that relates the Slutsky matrix to spontaneous fluctuations of consumption rather than to response to changing prices and budget. We then show that, within our hypotheses, the symmetry of the Slutsky matrix remains valid even when agents are only boundedly rational but non-interacting. We then propose a model where agents are influenced by the choice of others, leading to a phase transition beyond which consumption is dominated by herding (or `"fashion") effects. In this case, the individual Slutsky matrix is no longer symmetric, even for fully rational agents. The vicinity of the transition features a peak in asymmetry."

--- Maybe a mathed-up version of Becker?]]></description>
<dc:subject>economics fluctuation-response stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:04ead244e64d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:economics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fluctuation-response"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.15227">
    <title>[2205.15227] Geometrical approach to excess/housekeeping entropy production in discrete systems</title>
    <dc:date>2022-06-09T08:26:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.15227</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a geometrical excess/housekeeping decomposition of the entropy production for discrete systems such as Markov jump processes and chemical reaction networks. Unlike the Hatano-Sasa approach, our decomposition is always well defined, including in chemical systems that do not obey complex balance and may not have a stable steady state. We provide refinements of previously known thermodynamic uncertainty relations, including short- and finite-time relations in a Markov jump process, and a short-time relation in chemical reaction networks. In addition, our housekeeping term can be divided into cyclic contributions, thus generalizing Schnakenberg's cyclic decomposition of entropy production beyond steady states. Finally, we extend optimal transport theory by providing a thermodynamic speed limit for the L2-Wasserstein distance that holds in the absence of detailed balance or even a stable steady state."]]></description>
<dc:subject>to:NB statistical_mechanics stochastic_processes information_theory non-equilibrium</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dc284accc571/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2112.14721">
    <title>[2112.14721] Decomposing the local arrow of time in interacting systems</title>
    <dc:date>2022-06-09T08:22:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2112.14721</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We show that the evidence for a local arrow of time, which is equivalent to the entropy production in thermodynamic systems, can be decomposed. In a system with many degrees of freedom, there is a term that arises from the irreversible dynamics of the individual variables, and then a series of non--negative terms contributed by correlations among pairs, triplets, and higher--order combinations of variables. We illustrate this decomposition on simple models of noisy logical computations, and then apply it to the analysis of patterns of neural activity in the retina as it responds to complex dynamic visual scenes. We find that neural activity breaks detailed balance even when the visual inputs do not, and that this irreversibility arises primarily from interactions between pairs of neurons."

--- I presume this is the PRL.]]></description>
<dc:subject>to:NB information_theory entropy stochastic_processes non-equilibrium bialek.william</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3abdcc7647cd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bialek.william"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.01916">
    <title>[2203.01916] Emergence of local irreversibility in complex interacting systems</title>
    <dc:date>2022-06-09T08:21:40+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.01916</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the local evidence for the arrow of time, which is the entropy production for thermodynamic systems, can be decomposed. First, it can be split into two components: an independent term reflecting the dynamics of individual elements and an interaction term driven by the dependencies among elements. Adapting tools from non--equilibrium physics, we further decompose the interaction term into contributions from pairs of elements, triplets, and higher--order terms. We illustrate our methods on models of cellular sensing and logical computations, as well as on patterns of neural activity in the retina as it responds to visual inputs. We find that neural activity can define the arrow of time even when the visual inputs do not, and that the dominant contribution to this breaking of detailed balance comes from interactions among pairs of neurons."

--- I presume this is the PRE.]]></description>
<dc:subject>to:NB information_theory entropy stochastic_processes bialek.william non-equilibrium</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:eadd1135d83f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bialek.william"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.03769">
    <title>[2206.03769] Renormalization group and generalized Central Limit Theorems: The critical probability distributions of the order parameter of the Ising model</title>
    <dc:date>2022-06-09T08:20:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.03769</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We show that the functional renormalization group (FRG) allows for the generalization of the central limit theorem to strongly correlated random variables. On the example of the three-dimensional Ising model at criticality and using the simplest implementation of the FRG, we compute the probability distribution functions of the order parameter or equivalently its logarithm, called the rate functions in large deviations theory. We compute the entire family of universal scaling functions, obtained in the limit where the system size L and the correlation length of the infinite system ξ∞ diverge, with the ratio ζ=L/ξ∞ held fixed. It compares very accurately with numerical simulations."]]></description>
<dc:subject>to:NB stochastic_processes random_fields central_limit_theorem ising_model renormalization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0ddadeac6846/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ising_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:renormalization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.04163">
    <title>[2203.04163] Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chains</title>
    <dc:date>2022-06-09T08:19:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.04163</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Two recent and seemingly-unrelated techniques for proving mixing bounds for Markov chains are: (i) the framework of Spectral Independence, introduced by Anari, Liu and Oveis Gharan, and its numerous extensions, which have given rise to several breakthroughs in the analysis of mixing times of discrete Markov chains and (ii) the Stochastic Localization technique which has proven useful in establishing mixing and expansion bounds for both log-concave measures and for measures on the discrete hypercube. In this paper, we introduce a framework which connects ideas from both techniques. Our framework unifies, simplifies and extends those two techniques. In its center is the concept of a localization scheme which, to every probability measure, assigns a martingale of probability measures which localize in space as time evolves. As it turns out, to every such scheme corresponds a Markov chain, and many chains of interest appear naturally in this framework. This viewpoint provides tools for deriving mixing bounds for the dynamics through the analysis of the corresponding localization process. Generalizations of concepts of Spectral Independence and Entropic Independence naturally arise from our definitions, and in particular we recover the main theorems in the spectral and entropic independence frameworks via simple martingale arguments (completely bypassing the need to use the theory of high-dimensional expanders). We demonstrate the strength of our proposed machinery by giving short and (arguably) simpler proofs to many mixing bounds in the recent literature, including giving the first O(nlogn) bound for the mixing time of Glauber dynamics on the hardcore-model (of arbitrary degree) in the tree-uniqueness regime."]]></description>
<dc:subject>to:NB stochastic_processes mixing markov_models martingales</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:03c6185cd447/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://infostructuralist.wordpress.com/2021/09/02/sampling-using-diffusion-processes-from-langevin-to-schrodinger/">
    <title>Sampling Using Diffusion Processes, from Langevin to Schrödinger – The Information Structuralist</title>
    <dc:date>2022-06-05T15:48:25+00:00</dc:date>
    <link>https://infostructuralist.wordpress.com/2021/09/02/sampling-using-diffusion-processes-from-langevin-to-schrodinger/</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>stochastic_processes have_read simulation monte_carlo stochastic_differential_equations control_theory_and_control_engineering raginsky.maxim re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:697eaf9da922/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1605.08070">
    <title>[1605.08070] Nonlinear Stochastic Dynamics of Complex Systems, I: A Chemical Reaction Kinetic Perspective with Mesoscopic Nonequilibrium Thermodynamics</title>
    <dc:date>2022-03-02T15:14:03+00:00</dc:date>
    <link>https://arxiv.org/abs/1605.08070</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity, but population wise with statistical rate laws in their syntheses, degradations, spatial diffusion, individual state transitions, and interactions. Such a formal kinetic system in a small volume V, like a single cell, can be rigorously treated in terms of a Markov process describing its nonlinear kinetics as well as nonequilibrium thermodynamics at a mesoscopic scale. We introduce notions such as open, driven chemical systems, entropy production, free energy dissipation, etc. Then in the macroscopic limit, we illustrate how two new "laws", in terms of a generalized free energy of the mesoscopic stochastic dynamics, emerge. Detailed balance and complex balance are two special classes of "simple" nonlinear kinetics. Phase transition is intrinsically related to multi-stability and saddle-node bifurcation phenomenon, in the limits of time t→∞ and system's size V→∞. Using this approach, we re-articulate the notion of inanimate equilibrium branch of a system and nonequilibrium state of a living matter, as originally proposed by Nicolis and Prigogine, and seek a logic consistency between this viewpoint and that of P. W. Anderson and J. J. Hopfield's in which macroscopic law emerges through symmetry breaking."]]></description>
<dc:subject>to:NB via:vaguery non-equilibrium stochastic_processes statistical_mechanics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:51e1f55ad964/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:vaguery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://oxford.universitypressscholarship.com/view/10.1093/oso/9780192844507.001.0001/oso-9780192844507?rskey=nzm83v&amp;result=113">
    <title>Stochastic Limit Theory: An Introduction for Econometricians - Oxford Scholarship</title>
    <dc:date>2022-01-12T02:14:25+00:00</dc:date>
    <link>https://oxford.universitypressscholarship.com/view/10.1093/oso/9780192844507.001.0001/oso-9780192844507?rskey=nzm83v&amp;result=113</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first provides a handbook and reference for the underlying mathematics (Part I, Chapters 1–6), statistical theory (Part II, Chapters 7–11), and stochastic process theory (Part III, Chapters 12–18). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 19–22), the central limit theorem (Part V, Chapters 23–26), and the functional central limit theorem (Part VI, Chapters 27–32). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results."

--- Revised, 2021 edition of what I've often seen cited as a standard reference, but never read.]]></description>
<dc:subject>to:NB books:noted stochastic_processes convergence_of_stochastic_processes asymptotics ergodic_theory martingales mixing to_download</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:51efb0da9d46/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convergence_of_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:asymptotics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_download"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2110.04338">
    <title>[2110.04338] Learning from non-irreducible Markov chains</title>
    <dc:date>2021-10-18T13:52:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.04338</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Most of the existing literature on supervised learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical supervised learning problems are characterized by temporal dependence and strong correlation between the marginals of the data-generating process, suggesting that the i.i.d. assumption is not always justified. This problem has been already considered in the context of Markov chains satisfying the Doeblin condition. This condition, among other things, implies that the chain is not singular in its behavior, i.e. it is irreducible. In this article, we focus on the case when the training data set is drawn from a not necessarily irreducible Markov chain. Under the assumption that the chain is uniformly ergodic with respect to the L1-Wasserstein distance, and certain regularity assumptions on the hypothesis class and the state space of the chain, we first obtain a uniform convergence result for the corresponding sample error, and then we conclude learnability of the approximate sample error minimization algorithm and find its generalization bounds. At the end, a relative uniform convergence result for the sample error is also discussed."]]></description>
<dc:subject>to:NB markov_models stochastic_processes learning_theory learning_under_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:784109e439d5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2108.01657">
    <title>[2108.01657] Socioeconomic Clustering and Racial Segregation on Lattices with Heterogeneous Sites</title>
    <dc:date>2021-08-06T15:38:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2108.01657</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Schelling model of segregation moves colored agents on the vertices of a graph, with unhappy agents trying to move to new positions if the number of their neighbors with a different color exceeds some threshold. In this work, we consider race and socioeconomic status simultaneously to understand how carefully architected placement of urban infrastructure might affect segregation. We designate certain vertices on the graph as "urban sites", providing civic infrastructure that most benefits the poorer population. Infrastructure that is centralized, like a city center or mall, encourages poor agents to cluster centrally in addition to their homophily preferences for the same-colored neighbors, while infrastructure that is well distributed, like a large grid of inner-city bus routes, tends to disperse the low-income agents. We ask what effect these two scenarios have on segregation. We prove that centralized infrastructure simultaneously causes segregation and the "urbanization of poverty" (i.e., occupation of urban sites primarily by poor agents) when the homophily and incentives drawing the poor to urban sites are large enough. Moreover, even when homophily preferences are very small, as long as the incentives drawing the poor to urban sites is large, under income inequality where one race has a higher proportion of the poor, we get racial segregation on urban sites but integration on non-urban sites. However, we find overall mitigation of segregation when the urban sites are distributed throughout the graph and the incentive drawing the poor on the urban sites exceeds the homophily preference. We prove that in this case, no matter how strong homophily preferences are, it will be exponentially unlikely that a configuration chosen from stationarity will have large, homogeneous clusters of similarly colored agents, thus promoting integration in the city with high probability."]]></description>
<dc:subject>to:NB schelling_model stochastic_processes randall.dana</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1b580439f12d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:schelling_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:randall.dana"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.14268">
    <title>[2107.14268] Virtual Markov chains</title>
    <dc:date>2021-08-03T04:43:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.14268</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce the space of virtual Markov chains (VMCs) as a projective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual permutations is the projective limit of the spaces of all permutations of finite sets. We introduce the notions of virtual initial distribution (VID) and a virtual transition matrix (VTM), and we show that the law of any VMC is uniquely characterized by a pair of a VID and VTM which have to satisfy a certain compatibility condition. Lastly, we study various properties of compact convex sets associated to the theory of VMCs, including that the Birkhoff-von Neumann theorem fails in the virtual setting."]]></description>
<dc:subject>to:NB stochastic_processes markov_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:310141c80200/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.13837">
    <title>[2107.13837] A general Kolmogorov-Chentsov type theorem with applications to limit theorems for Banach-valued processes</title>
    <dc:date>2021-07-30T02:52:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.13837</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper deals with moduli of continuity for paths of random processes with outcomes in general metric spaces. Adapting the moment condition on the increments from the classical Kolmogorov-Chentsov theorem, the obtained result on the modulus of continuity allows for Hoelder-continuous modifications if the metric spaces are complete. This result is universal in the sense that its applicability depends only on the geometry of the parametric spaces. In particular, it is always applicable if parametric spaces are bounded subsets of Euclidean spaces. The derivation is based on refined chaining techniques developed by Talagrand. As a consequence of the main result a criterion is presented to guarantee uniform tightness of random processes with continuous paths. This is applied to find central limit theorems for Banach-valued random processes."]]></description>
<dc:subject>to:NB stochastic_processes re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1fb1ee744cd0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.13197">
    <title>[2107.13197] The stationary and quasi-stationary properties of neutral multi-type branching process diffusions</title>
    <dc:date>2021-07-29T17:35:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.13197</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions conditioned on non-extinction. Limiting distributions for supercritical and critical processes are found to collapse onto rays aligned with stationary eigenvectors of the mutation rate matrix, in agreement with known results for discrete multi-type branching processes. For the sub-critical process the quasi-stationary distribution is obtained to first order in the overall mutation rate, which is assumed to be small. The sampling distribution over allele types for a sample of given finite size is found to agree to first order in mutation rates with the analogous sampling distribution for a Wright-Fisher diffusion with constant population size."]]></description>
<dc:subject>branching_processes stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f831a47707e4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:branching_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.08469">
    <title>[2107.08469] Quantitative Marcinkiewicz's theorem and central limit theorems: applications to spin systems and point processes</title>
    <dc:date>2021-07-27T12:05:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.08469</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The classical Marcinkiewicz theorem states that if an entire characteristic function Ψ of a non-degenerate real-valued random variable X is of the form exp(P(u)) for some polynomial P, then X has to be a Gaussian. In this work, we obtain a broad, quantitative extension of this framework in several directions, establish central limit theorems (CLTs) with explicit rates of convergence, and demonstrate Gaussian fluctuations in continuous spin systems and general classes of point processes. In particular, we obtain quantitative decay estimates on the Kolmogorov-Smirnov distance between X and a Gaussian under the condition that Ψ does not vanish only on a bounded disk. This leads to quantitative CLTs applicable to very general and possibly strongly dependent random systems. In spite of the general applicability, our rates for the CLT match the classic Berry-Esseen bounds for independent sums up to a log factor. We implement this programme for two important classes of models in probability and statistical physics. First, we extend to the setting of continuous spins a popular paradigm for obtaining CLTs for discrete spin systems that is based on the theory of Lee-Yang zeros, focussing in particular on the XY model, Heisenberg ferromagnets and generalised Ising models. Secondly, we establish Gaussian fluctuations for linear statistics of so-called α-determinantal processes for α∈ℝ (including the usual determinantal, Poisson and permanental processes) under very general conditions, including in particular higher dimensional settings where structural alternatives such as random matrix techniques are not available. Our applications demonstrate the significance of having to control the characteristic function only on a (small) disk, and lead to CLTs which, to the best of our knowledge, are not known in generality."]]></description>
<dc:subject>to:NB probability stochastic_processes central_limit_theorem point_processes statistical_mechanics re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9bb1f648cb93/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:point_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1912.07951">
    <title>[1912.07951] Causal Functional Calculus</title>
    <dc:date>2021-07-22T15:43:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1912.07951</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We construct a new topology on the space of right continuous paths with left limits (cadlag paths) and introduce a calculus for causal functionals on generic domains of this space. We propose a general approach to pathwise integration without any assumption on the variation index of the paths and obtain functional change of variable formulas which extend the results of H. Foellmer (1981) and Cont & Fournie (2010) to a larger class of functionals, including Foellmer's pathwise integrals. In particular we introduce a class of functionals which satisfy a pathwise analogue of the martingale property.
"In the case of paths with finite quadratic variation along a partition sequence, our formula extends the Foellmer-Ito calculus and relaxes previous assumptions relating the partition sequence to the discontinuities of the underlying path. We introduce a foliation structure on the space of cadlag paths with finite quadratic variation and show that harmonic functionals may be represented as restrictions of pathwise integrals of closed 1-forms."]]></description>
<dc:subject>to:NB stochastic_processes martingales statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fbe807557e5d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2002.05423">
    <title>[2002.05423] Spatial birth-death-move processes : basic properties and estimation of their intensity functions</title>
    <dc:date>2021-07-14T04:15:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2002.05423</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications include epidemiology, individual-based modelling in ecology, spatio-temporal dynamics observed in bio-imaging, and computer vision. The aim of this article is to estimate in this context the birth and death intensity functions, that depend in full generality on the current spatial configuration of all alive individuals. While the temporal evolution of the population size is a simple birth-death process, observing the lifetime and trajectories of all individuals calls for a new paradigm. To formalise this framework, we introduce spatial birth-death-move processes, where the birth and death dynamics depends on the current spatial configuration of the population and where individuals can move during their lifetime according to a continuous Markov process with possible interactions.We consider non-parametric kernel estimators of their birth and death intensity functions. The setting is original because each observation in time belongs to a non-vectorial, infinite dimensional space and the dependence between observations is barely tractable. We prove the consistency of the estimators in presence of continuous-time and discrete-time observations, under fairly simple conditions. We moreover discuss how we can take advantage in practice of structural assumptions made on the intensity functions and we explain how data-driven bandwidth selection can be conducted, despite the unknown (and sometimes undefined) second order moments of the estimators. We finally apply our statistical method to the analysis of the spatio-temporal dynamics of proteins involved in exocytosis in cells, providing new insights on this complex mechanism."]]></description>
<dc:subject>to:NB stochastic_processes point_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8ff2df876feb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:point_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.04351">
    <title>[2107.04351] Breaking of ensemble equivalence for dense random graphs under a single constraint</title>
    <dc:date>2021-07-12T15:20:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.04351</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Two ensembles are often used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is said that breaking of ensemble equivalence (BEE) occurs when the specific relative entropy of the two ensembles does not vanish as the size of the graph tends to infinity. The latter means that it matters for the scaling properties of the graph whether the constraint is met for every single realisation of the graph or only holds as an ensemble average. In the literature, it was found that BEE is the rule rather than the exception for two classes: sparse random graphs when the number of constraints is of the order of the number of vertices and dense random graphs when there are two or more constraints that are frustrated. In the present paper we establish BEE for a third class: dense random graphs with a single constraint, namely, on the density of a given finite simple graph. We show that BEE occurs only in a certain range of choices for the density and the number of edges of the simple graph, which we refer to as the BEE-phase. We show that, in part of the BEE-phase, there is a gap between the scaling limits of the averages of the maximal eigenvalue of the adjacency matrix of the random graph under the two ensembles, a property that is referred to as spectral signature of BEE. Proofs are based on an analysis of the variational formula on the space of graphons for the limiting specific relative entropy derived by Den Hollander et al. (2018), in combination with an identification of the minimising graphons and replica symmetry arguments. We show that in the replica symmetric region of the BEE-phase, as the size of the graph tends to infinity, the microcanonical ensemble behaves like an Erdős-Rényi random graph, while the canonical ensemble behaves like a mixture of two Erdős-Rényi random graphs."]]></description>
<dc:subject>to:NB graphons statistical_mechanics stochastic_processes den_hollander.frank</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9d69e814495d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphons"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:den_hollander.frank"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.03975">
    <title>[2107.03975] Compressibility Analysis of Asymptotically Mean Stationary Processes</title>
    <dc:date>2021-07-11T05:55:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.03975</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This work provides new results for the analysis of random sequences in terms of ℓp-compressibility. The results characterize the degree in which a random sequence can be approximated by its best k-sparse version under different rates of significant coefficients (compressibility analysis). In particular, the notion of strong ℓp-characterization is introduced to denote a random sequence that has a well-defined asymptotic limit (sample-wise) of its best k-term approximation error when a fixed rate of significant coefficients is considered (fixed-rate analysis). The main theorem of this work shows that the rich family of asymptotically mean stationary (AMS) processes has a strong ℓp-characterization. Furthermore, we present results that characterize and analyze the ℓp-approximation error function for this family of processes. Adding ergodicity in the analysis of AMS processes, we introduce a theorem demonstrating that the approximation error function is constant and determined in closed-form by the stationary mean of the process. Our results and analyses contribute to the theory and understanding of discrete-time sparse processes and, on the technical side, confirm how instrumental the point-wise ergodic theorem is to determine the compressibility expression of discrete-time processes even when stationarity and ergodicity assumptions are relaxed."]]></description>
<dc:subject>to:NB stochastic_processes sparsity approximation ergodic_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:485fccb044e3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.16201">
    <title>[2106.16201] Evolving genealogies for branching populations under selection and competition</title>
    <dc:date>2021-07-01T15:50:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.16201</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the unique strong solution of a system of SDE's. Our construction is achieved in the lookdown framework and provides a synthesis as well as a generalization of cases considered separately in two seminal papers by Donnelly and Kurtz (1999), namely fluctuating population sizes under neutrality, and selection with constant population size. As a conceptual core in our approach, we introduce the selective lookdown space which is obtained from its neutral counterpart through a state-dependent thinning of "potential" selection/competition events whose rates interact with the evolution of the type densities. The updates of the genealogical distance matrix at the "active" selection/competition events are obtained through an appropriate sampling from the selective lookdown space. The solution of the above mentioned system of SDE's is then mapped into the joint evolution of population size and symmetrized type configurations and genealogies, i.e. marked distance matrix distributions. By means of Kurtz's Markov mapping theorem, we characterize the latter process as the unique solution of a martingale problem. For the sake of transparency we restrict the main part of our presentation to a prototypical example with two types, which contains the essential features. In the final section we outline an extension to processes with multiple types including mutation."]]></description>
<dc:subject>to:NB evolutionary_biology branching_processes stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f8347b059c16/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:evolutionary_biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:branching_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.14990">
    <title>[2106.14990] Committor Functions for Climate Phenomena at the Predictability Margin: The example of El Niño Southern Oscillation in the Jin and Timmerman model</title>
    <dc:date>2021-06-30T18:44:05+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.14990</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many phenomena in the climate system lie in the gray zone between weather and climate: they are not amenable to deterministic forecast, but they still depend on the initial condition. A natural example is medium-range forecasting, which is inherently probabilistic because it lies beyond the deterministic predictability time of the atmosphere, but for which statistically significant prediction can be made which depend on the current state of the system. Similarly, one may ask the probability of occurrence of an El Niño event several months ahead of time. In this paper, we introduce a quantity which corresponds precisely to this type of prediction problem: the committor function is the probability that an event takes place within a given time window, as a function of the initial condition. We explain the main mathematical properties of this probabilistic concept, and compute it in the case of a low-dimensional stochastic model for El-Niño, the Jin and Timmerman model. In this context, we show that the ability to predict the probability of occurrence of the event of interest may differ strongly depending on the initial state. The main result is the new distinction between intrinsic probabilistic predictability (when the committor function is smooth and probability can be computed which does not depend sensitively on the initial condition) and intrinsic probabilistic unpredictability (when the committor function depends sensitively on the initial condition). We also demonstrate that the Jin and Timmerman model might be the first example of a stochastic differential equation with weak noise for which transition between attractors do not follow the Arrhenius law, which is expected based on large deviation theory and generic hypothesis."]]></description>
<dc:subject>to:NB prediction climatology stochastic_processes bouchet.freddy to_read statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:171390f4e0e1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:climatology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bouchet.freddy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.062144">
    <title>Phys. Rev. E 103, 062144 (2021) - Optimal sampling of dynamical large deviations via matrix product states</title>
    <dc:date>2021-06-30T02:48:54+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.062144</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called “Doob”) dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions."]]></description>
<dc:subject>stochastic_processes large_deviations computational_statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cc21cec0a6f0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.08525">
    <title>[2106.08525] A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions</title>
    <dc:date>2021-06-28T04:35:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.08525</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this article, we prove a Feynman-Kac type result for a broad class of second order ordinary differential equations. The classical Feynman-Kac theorem says that the solution to a broad class of second order parabolic equations is the mean of a particular diffusion. In our situation, we show that the solution to a system of second order ordinary differential equations is the mode of a diffusion, defined through the Onsager-Machlup formalism. One potential utility of our result is to use Monte Carlo type methods to estimate the solutions of ordinary differential equations. We conclude with examples of our result illustrating its utility in numerically solving linear second order ODEs."]]></description>
<dc:subject>to:NB stochastic_processes dynamical_systems path_integrals_for_classical_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a427215fa02e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:path_integrals_for_classical_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.10834">
    <title>[2102.10834] Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models</title>
    <dc:date>2021-06-28T04:33:39+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.10834</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Ruelle thermodynamic formalism for dynamical trajectories over the large time T corresponds to the large deviation theory for the information per unit time of the trajectories probabilities. The microcanonical analysis consists in evaluating the exponential growth in T of the number of trajectories with a given information per unit time, while the canonical analysis amounts to analyze the appropriate non-conserved β-deformed dynamics in order to obtain the scaled cumulant generating function of the information, the first cumulant being the famous Kolmogorov-Sinai entropy. This framework is described in detail for discrete-time Markov chains and for continuous-time Markov jump processes converging towards some steady-state, where one can also construct the Doob generator of the associated β-conditioned process. The application to the Directed Random Trap model on a ring of L sites allows to illustrate this general framework via explicit results for all the introduced notions. In particular, the glassy phase is characterized by anomalous scaling laws with the size L and by non-self-averaging properties of the Kolmogorov-Sinai entropy and of the higher cumulants of the trajectory information."]]></description>
<dc:subject>to:NB large_deviations stochastic_processes statistical_mechanics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4273cf3c5937/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>