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    <description>recent bookmarks from cshalizi</description>
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  </channel><item rdf:about="https://www.jstor.org/stable/1403785?seq=1">
    <title>Markov and the Birth of Chain Dependence Theory on JSTOR</title>
    <dc:date>2026-06-01T13:58:12+00:00</dc:date>
    <link>https://www.jstor.org/stable/1403785?seq=1</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>in_NB markov_models history_of_mathematics markov.a.a. ergodic_theory mixing free_will</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b76b51010206/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:history_of_mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov.a.a."/>
	<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:free_will"/>
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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>
<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03529-3">
    <title>Complete Ergodicity in One-Dimensional Reversible Cellular Automata | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:21:36+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03529-3</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 18 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure."]]></description>
<dc:subject>to:NB cellular_automata ergodic_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bbc72756bc1b/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cellular_automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
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</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03453-6">
    <title>A Path Method for Non-exponential Ergodicity of Markov Chains and Its Application for Chemical Reaction Systems | Journal of Statistical Physics</title>
    <dc:date>2025-07-08T15:28:11+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03453-6</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space in total variation norm. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this path method to explore the non-exponential convergence of microscopic biochemical interacting systems. Using reaction network descriptions, we identified special architectures of biochemical systems for non-exponential ergodicity. In essence, we found that reactions forming a cycle in the reaction network can induce non-exponential ergodicity when they significantly dominate other reactions across infinitely many regions of the state space. Interestingly, the special architectures allowed us to construct many detailed balanced and complex balanced biochemical systems that are non-exponentially ergodic. Some of these models are low-dimensional bimolecular systems with few reactions. Thus this work suggests the possibility of discovering or synthesizing stochastic systems arising in biochemistry that possess either detailed balancing or complex balancing and slowly converge to their stationary distribution."]]></description>
<dc:subject>in_NB markov_models ergodic_theory chemistry</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:47b10b880d00/</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:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chemistry"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2203.04395">
    <title>[2203.04395] Equivalences of Geometric Ergodicity of Markov Chains</title>
    <dc:date>2024-12-11T16:02:48+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.04395</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper gathers together different conditions which are all equivalent to geometric ergodicity of time-homogeneous Markov chains on general state spaces. A total of 34 different conditions are presented (27 for general chains plus 7 just for reversible chains), some old and some new, in terms of such notions as convergence bounds, drift conditions, spectral properties, etc., with different assumptions about the distance metric used, finiteness of function moments, initial distribution, uniformity of bounds, and more. Proofs of the connections between the different conditions are provided, mostly self-contained but using some results from the literature where appropriate."]]></description>
<dc:subject>to:NB markov_models mixing ergodic_theory re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bb278df058e6/</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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
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</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>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
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</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://notstatschat.rbind.io/2022/09/28/uniform-law-of-large-numbers/">
    <title>A plug-in uniform law of large numbers - Biased and Inefficient</title>
    <dc:date>2023-06-15T19:18:32+00:00</dc:date>
    <link>https://notstatschat.rbind.io/2022/09/28/uniform-law-of-large-numbers/</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>have_read ergodic_theory empirical_processes lumley.thomas learning_theory re:HEAS in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1dfcf0d1d3f9/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lumley.thomas"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:HEAS"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2305.05028">
    <title>[2305.05028] Non-stationary version of Ergodic Theorem for random dynamical systems</title>
    <dc:date>2023-06-08T15:27:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2305.05028</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We prove a version of pointwise Ergodic Theorem for non-stationary random dynamical systems. Also, we discuss two specific examples where the result is applicable: non-stationary iterated function systems and non-stationary random matrix products."

--- To check: is this just an asymptotically-mean-stationary ergodic theorem (as in, e.g., Grey), or something genuinely stronger?]]></description>
<dc:subject>non-stationarity ergodic_theory to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e9ae3f2b3295/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<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://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/2203.09085">
    <title>[2203.09085] A Simple Non-Stationary Mean Ergodic Theorem, with Bonus Weak Law of Large Numbers</title>
    <dc:date>2022-03-20T21:17:33+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.09085</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This brief pedagogical note re-proves a simple theorem on the convergence, in L2 and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances grows sub-quadratically with the length of the time series. I make no claim to originality; the result is widely, but unevenly, spread bit of folklore among users of applied probability. The goal of this note is merely to even out that distribution."]]></description>
<dc:subject>ergodic_theory self-promotion to:blog</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9ae05c041970/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-promotion"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
</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/2108.00997">
    <title>[2108.00997] Generalization bounds for nonparametric regression with $β-$mixing samples</title>
    <dc:date>2021-08-11T18:56:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2108.00997</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of β−mixing coefficients associated to the training sample. We then apply these results to some previously obtained inequalities for independent samples associated to the deviation of the least-squared error in nonparametric regression to derive corresponding generalization bounds for regression schemes in which the training sample may not be independent.
"These results provide a framework to analyze the error associated to regression schemes whose training sample comes from a large class of β−mixing sequences, including geometrically ergodic Markov samples, using only the independent case. More generally, they permit a meaningful extension of the Vapnik-Chervonenkis and similar theories for independent training samples to this class of β−mixing samples."

--- From the abstract, I don't understand how this differs from what Yu, Vidyasagar &c. did back in the early 1990s, so there has to be more.]]></description>
<dc:subject>in_NB to_read learning_theory ergodic_theory mixing statistics learning_under_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5d2f8d41532e/</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:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<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:statistics"/>
	<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/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/2106.00177">
    <title>[2106.00177] Solutions of the Multivariate Inverse Frobenius--Perron Problem</title>
    <dc:date>2021-07-01T13:31:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.00177</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We address the inverse Frobenius--Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map, that is, a map under which the uniform distribution on the d-dimensional hypercube as invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via 1-dimensional examples, and then use the factorization to present solutions in 1 and 2 dimensions induced by a range of uniform maps."]]></description>
<dc:subject>to:NB dynamical_systems ergodic_theory computational_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cc12c18854a0/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-071020-010108">
    <title>Koopman Operators for Estimation and Control of Dynamical Systems | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2021-05-06T13:46:57+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-071020-010108</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A common way to represent a system's dynamics is to specify how the state evolves in time. An alternative viewpoint is to specify how functions of the state evolve in time. This evolution of functions is governed by a linear operator called the Koopman operator, whose spectral properties reveal intrinsic features of a system. For instance, its eigenfunctions determine coordinates in which the dynamics evolve linearly. This review discusses the theoretical foundations of Koopman operator methods, as well as numerical methods developed over the past two decades to approximate the Koopman operator from data, for systems both with and without actuation. We pay special attention to ergodic systems, for which especially effective numerical methods are available. For nonlinear systems with an affine control input, the Koopman formalism leads naturally to systems that are bilinear in the state and the input, and this structure can be leveraged for the design of controllers and estimators."

]]></description>
<dc:subject>dynamical_systems control_theory_and_control_engineering ergodic_theory in_NB koopman_operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:adc64525a4f6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:koopman_operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.08641">
    <title>[1901.08641] Gibbs posterior convergence and the thermodynamic formalism</title>
    <dc:date>2020-12-12T20:03:25+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.08641</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard Bayesian inference. We place a prior over a model class consisting of a parametrized family of Gibbs measures on a mixing shift of finite type. This model class generalizes (hidden) Markov chain models by allowing for long range dependencies, including Markov chains of arbitrarily large orders. We characterize the asymptotic behavior of the Gibbs posterior distribution on the parameter space as the number of observations tends to infinity. In particular, we define a limiting variational problem over the space of joinings of the model system with the observed system, and we show that the Gibbs posterior distributions concentrate around the solution set of this variational problem. In the case of properly specified models our convergence results may be used to establish posterior consistency. This work establishes tight connections between Gibbs posterior inference and the thermodynamic formalism, which may inspire new proof techniques in the study of Bayesian posterior consistency for dependent processes."]]></description>
<dc:subject>to:NB bayesian_consistency statistical_inference_for_stochastic_processes dynamical_systems large_deviations ergodic_theory nobel.andrew</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2ed738a0f046/</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:bayesian_consistency"/>
	<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:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nobel.andrew"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.jstor.org/stable/j.ctt7rwxj">
    <title>The Ergodic Theory of Lattice Subgroups (AM-172) on JSTOR</title>
    <dc:date>2020-01-26T17:18:14+00:00</dc:date>
    <link>https://www.jstor.org/stable/j.ctt7rwxj</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to:NB books:noted ergodic_theory downloaded</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7b0c4501650e/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.nature.com/articles/s41567-019-0732-0">
    <title>The ergodicity problem in economics | Nature Physics</title>
    <dc:date>2019-12-06T17:57:25+00:00</dc:date>
    <link>https://www.nature.com/articles/s41567-019-0732-0</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[I find this intensely disappointing.
(I) We know, experimentally, that people do not maximize _ex ante_ expected utility.
(II) The decision rule that is supposed to be replacing "maximize expected utility" is, evidently, "maximize the growth rate of wealth", i.e., "maximize the long-run average increment to log wealth".
  A. So why isn't this is just re-inventing Kelly gambling?  (Yes, Kelly is cited.)
  B. For the long-run growth rate of wealth to be a uniquely-defined quantity  _presumes_ ergodicity for for the increments of log-wealth. If increments to log-wealth are stationary but not ergodic, this time average converges to a random quantity; if log wealth is an I(2) process (or higher-order integrated process), then it won't converge at all.  The rule "pick the option with the higher long-run time-average growth rate" is therefore insufficient, and we do not see what "ergodicity economics" predicts (or advises) in some very basic situations.  (These situations just happen not to include geometric Brownian motion.)
(III) Presuming that the time-average growth rate of wealth converges, the decision maker does not necessarily _know_ what it will converge _to_.  This is a fundamental problem of decision-making under _uncertainty_, as opposed to stochastic _risk_.  All of the examples presume the data-generating process is completely known to the decision-maker, which is an extremely strong form of rational expectations.  What does "ergodicity economics" predict about choosing between two GBMs with uncertainty about the growth rate?
]]></description>
<dc:subject>economics ergodic_theory decision_theory my_initial_skeptical_coloration_became_on_examination_a_permanent_stain</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1ed7cdb276ce/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:decision_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:my_initial_skeptical_coloration_became_on_examination_a_permanent_stain"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1903.01059">
    <title>[1903.01059] Limit Theorems for Network Dependent Random Variables</title>
    <dc:date>2019-10-01T16:18:24+00:00</dc:date>
    <link>https://arxiv.org/abs/1903.01059</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper considers a general form of network dependence where dependence between two sets of random variables becomes weaker as their distance in a network gets longer. We show that such network dependence cannot be embedded as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This paper applies Doukhan and Louhichi (1999)'s weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables. While this approach covers examples such as strong mixing random fields on a graph and conditional dependency graphs, it is most useful when dependence arises through a large functional-causal system of equations. The main results of our paper include the law of large numbers, and the central limit theorem. We also propose a heteroskedasticity-autocorrelation consistent variance estimator and prove its consistency under regularity conditions. The finite sample performance of this latter estimator is investigated through a Monte Carlo simulation study."]]></description>
<dc:subject>to:NB network_data_analysis ergodic_theory to_read probability statistics to_teach:baby-nets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a20daa664dfb/</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:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:baby-nets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.11453">
    <title>[1909.11453] A finitary factor of an i.i.d. process which is not finitarily Bernoulli</title>
    <dc:date>2019-09-26T18:18:19+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.11453</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We construct a finitary factor of an i.i.d. process which is not finitarily isomorphic to an i.i.d. process. This refutes a conjecture of M. Smorodinsky [11], which was first suggested by D. Rudolph [7]. We further show that any ergodic system is isomorphic to a process none of whose finitary factors are i.i.d. processes, and in particular, there is no general finitary Sinai's factor theorem for ergodic processes. An immidiate consequence of this result is the invalidity of a finitary weak Pinsker property, answering a question of G. Pete and T. Austin [1]."]]></description>
<dc:subject>to:NB stochastic_processes ergodic_theory symbolic_dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:37161bd4fb95/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.07363">
    <title>[1909.07363] On an irreducibility type condition for the ergodicity of nonconservative semigroups</title>
    <dc:date>2019-09-17T14:00:59+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.07363</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment."]]></description>
<dc:subject>to:NB ergodic_theory markov_models stochastic_processes re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3c54d60c247c/</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:ergodic_theory"/>
	<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:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.02375">
    <title>[1908.02375] Limit Theorems for Data with Network Structure</title>
    <dc:date>2019-08-08T13:12:21+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.02375</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation models are an example. Wether two data points are highly correlated or not depends on draws from underlying characteristics distributions. The paper defines a measure of closeness that depends on primitive conditions on the distribution of observable characteristics as well as functional form of the underlying model. A summability condition over the probability distribution of observable characteristics is shown to be a critical ingredient in establishing limit results. The paper establishes weak and strong laws of large numbers as well as a stable central limit theorem for a class of statistics that include as special cases network statistics such as average node degrees or average peer characteristics. Some worked examples illustrating the theory are provided."]]></description>
<dc:subject>to:NB stochastic_processes networks network_data_analysis ergodic_theory to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a521bf0aba6f/</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:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.01794">
    <title>[1908.01794] Some Developments in Clustering Analysis on Stochastic Processes</title>
    <dc:date>2019-08-07T12:29:36+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.01794</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the triangle inequality. Examples are provided when the processes are distribution ergodic, covariance ergodic and locally asymptotically self-similar, respectively."]]></description>
<dc:subject>to:NB stochastic_processes ergodic_theory clustering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fbbeae07f608/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:clustering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.00845">
    <title>[1908.00845] Iterations of dependent random maps and exogeneity in nonlinear dynamics</title>
    <dc:date>2019-08-05T14:13:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.00845</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We discuss existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated in the dynamic. To this end, we consider the convergence of the backward iterations of dependent random maps. In particular, we give a new result when the classical condition of contraction on average is replaced with a contraction in conditional expectation. Under some conditions, we also derive an explicit control of the functional dependence of Wu (2005) which guarantees a wide range of statistical applications. Our results are illustrated with CHARME models, GARCH processes, count time series, binary choice models and categorical time series for which we provide many extensions of existing results."]]></description>
<dc:subject>to:NB stochastic_processes ergodic_theory mixing time_series dynamical_systems statistics statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:47d385d293f6/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1907.13533">
    <title>[1907.13533] Coupling and perturbation techniques for categorical time series</title>
    <dc:date>2019-08-02T15:18:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1907.13533</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a general approach for studying autoregressive categorical time series models with dependence of infinite order and defined conditional on an exogenous covariate process. To this end, we adapt a coupling approach, developed in the literature for bounding the relaxation speed of a chain with complete connection and from which we derive a perturbation result for non-homogenous versions of such chains. We then study stationarity, ergodicity and dependence properties of some chains with complete connections and exogenous covariates. As a consequence, we obtain a general framework for studying some observation-driven time series models used both in statistics and econometrics but without theoretical support."]]></description>
<dc:subject>to:NB ergodic_theory chains_with_complete_connections time_series</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e3e4afc9bb18/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chains_with_complete_connections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://global.oup.com/academic/product/functional-gaussian-approximation-for-dependent-structures-9780198826941?cc=us&amp;lang=en#">
    <title>Functional Gaussian Approximation for Dependent Structures - Florence Merlevede; Magda Peligrad; Sergey Utev - Oxford University Press</title>
    <dc:date>2019-05-24T23:55:52+00:00</dc:date>
    <link>https://global.oup.com/academic/product/functional-gaussian-approximation-for-dependent-structures-9780198826941?cc=us&amp;lang=en#</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. 
"Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory.
"The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed."]]></description>
<dc:subject>to:NB central_limit_theorem stochastic_processes convergence_of_stochastic_processes mixing ergodic_theory re:almost_none books:noted</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a47e5db7c861/</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:convergence_of_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1602.06093">
    <title>[1602.06093] Self-organisation in cellular automata with coalescent particles: qualitative and quantitative approaches</title>
    <dc:date>2019-02-06T18:07:12+00:00</dc:date>
    <link>https://arxiv.org/abs/1602.06093</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial configuration at random according to some initial σ-ergodic measure μ, and use the limit measure to descrbe the asymptotic behaviour of the automata. We first take a qualitative approach, i.e. we obtain information on the limit measure(s). We prove that only particles moving in one particular direction can persist asymptotically. This provides some previously unknown information on the limit measures of various deterministic and probabilistic cellular automata: 3 and 4-cyclic cellular automata (introduced in [Fis90b]), one-sided captive cellular automata (introduced in [The04]), N. Fat{è}s' candidate to solve the density classification problem [Fat13], self stabilization process toward a discrete line [RR15]... In a second time we restrict our study to to a subclass, the gliders cellular automata. For this class we show quantitative results, consisting in the asymptotic law of some parameters: the entry times (generalising [KFD11]), the density of particles and the rate of convergence to the limit measure."]]></description>
<dc:subject>to:NB interacting_particle_systems cellular_automata ergodic_theory stochastic_processes via:vaguery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:040513c19009/</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:interacting_particle_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cellular_automata"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:vaguery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s2-20.1.196">
    <title>Diffusion by Continuous Movements - Taylor - 1922 - Proceedings of the London Mathematical Society - Wiley Online Library</title>
    <dc:date>2018-12-29T17:47:47+00:00</dc:date>
    <link>https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s2-20.1.196</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Apparently (?) the original source for what I've been calling the "world's simplest ergodic theorem" (http://bactra.org/weblog/668.html), and the associated calculation of the correlation time.  (This would explain why one of the places I learned it was Frisch's book on turbulence.)

--- Reference via Eshel's _Spatiotemporal Data Analysis_ (review forthcoming), though that mangled the bibliographic information.]]></description>
<dc:subject>stochastic_processes turbulence ergodic_theory probability have_skimmed taylor.g.i. physics re:almost_none to_teach:data_over_space_and_time in_NB have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:93f1a3437d1f/</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:turbulence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:taylor.g.i."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aop/1176996798#abstract">
    <title>Kingman : Subadditive Ergodic Theory</title>
    <dc:date>2018-06-02T16:41:05+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aop/1176996798#abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["It is now ten years since Hammersley and Welsh discovered (or invented) subadditive stochastic processes. Since then the theory has developed and deepened, new fields of application have been explored, and further challenging problems have arisen. This paper is a progress report on the last decade."]]></description>
<dc:subject>in_NB stochastic_processes ergodic_theory have_read re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9406a2c06f8b/</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: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:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mdpi.com/1099-4300/20/2/85">
    <title>Entropy | Free Full-Text | Is Natural Language a Perigraphic Process? The Theorem about Facts and Words Revisited</title>
    <dc:date>2018-03-06T16:01:04+00:00</dc:date>
    <link>http://www.mdpi.com/1099-4300/20/2/85</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[I don't understand how this definition is compatible with the ergodic decomposition.]]></description>
<dc:subject>information_theory formal_languages entropy_estimation algorithmic_information_theory ergodic_theory in_NB color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fcbefa1e4844/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:formal_languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algorithmic_information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springer.com/gp/book/9783319415963">
    <title>Random Measures, Theory and Applications | Olav Kallenberg | Springer</title>
    <dc:date>2017-09-13T22:40:57+00:00</dc:date>
    <link>http://www.springer.com/gp/book/9783319415963</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas."]]></description>
<dc:subject>to:NB books:noted probability stochastic_processes ergodic_theory kallenberg.olav coveted downloaded</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b02eee6d26ec/</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:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kallenberg.olav"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:coveted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springer.com/gp/book/9783662543221?wt_mc=Alerts.NBA.Sep-13">
    <title>Asymptotic Theory of Weakly Dependent Random Processes | Emmanuel Rio | Springer</title>
    <dc:date>2017-09-13T22:39:50+00:00</dc:date>
    <link>http://www.springer.com/gp/book/9783662543221?wt_mc=Alerts.NBA.Sep-13</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular.
"The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises.
"The book is an updated and extended translation of the French edition entitled "Théorie asymptotique des processus aléatoires faiblement dépendants" (Springer, 2000). It will be useful for students and researchers in mathematical statistics, econometrics, probability theory and dynamical systems who are interested in weakly dependent processes."]]></description>
<dc:subject>books:noted stochastic_processes mixing ergodic_theory markov_models in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6799ddedf364/</dc:identifier>
<taxo:topics><rdf:Bag>	<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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00870">
    <title>Learning Theory Estimates with Observations from General Stationary Stochastic Processes | Neural Computation | MIT Press Journals</title>
    <dc:date>2016-11-23T18:21:15+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00870</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using gaussian kernels for both least squares and quantile regression. It turns out that for independent and identically distributed (i.i.d.) processes, our learning rates for ERM recover the optimal rates. For non-i.i.d. processes, including geometrically -mixing Markov processes, geometrically -mixing processes with restricted decay, -mixing processes, and (time-reversed) geometrically -mixing processes, our learning rates for SVMs with gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called effective number of observations for various mixing processes."]]></description>
<dc:subject>stochastic_processes learning_theory dependence_measures mixing ergodic_theory statistics re:XV_for_mixing re:your_favorite_dsge_sucks in_NB 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:5c929691bae6/</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:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dependence_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:XV_for_mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:your_favorite_dsge_sucks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<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="http://cambridge.org/9781107126961">
    <title>Foundations of Ergodic Theory | Abstract Analysis | Cambridge University Press</title>
    <dc:date>2016-09-30T17:34:34+00:00</dc:date>
    <link>http://cambridge.org/9781107126961</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book."]]></description>
<dc:subject>ergodic_theory mathematics stochastic_processes probability books:noted re:almost_none in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4fd06d026b96/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<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="http://arxiv.org/abs/1308.4117">
    <title>[1308.4117] Comparison Theorems for Gibbs Measures</title>
    <dc:date>2016-09-07T14:49:37+00:00</dc:date>
    <link>http://arxiv.org/abs/1308.4117</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Dobrushin comparison theorem is a powerful tool to bound the difference between the marginals of high-dimensional probability distributions in terms of their local specifications. Originally introduced to prove uniqueness and decay of correlations of Gibbs measures, it has been widely used in statistical mechanics as well as in the analysis of algorithms on random fields and interacting Markov chains. However, the classical comparison theorem requires validity of the Dobrushin uniqueness criterion, essentially restricting its applicability in most models to a small subset of the natural parameter space. In this paper we develop generalized Dobrushin comparison theorems in terms of influences between blocks of sites, in the spirit of Dobrushin-Shlosman and Weitz, that substantially extend the range of applicability of the classical comparison theorem. Our proofs are based on the analysis of an associated family of Markov chains. We develop in detail an application of our main results to the analysis of sequential Monte Carlo algorithms for filtering in high dimension."]]></description>
<dc:subject>statistical_mechanics stochastic_processes ergodic_theory mixing van_handel.ramon in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:11c81a1313cd/</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:stochastic_processes"/>
	<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:van_handel.ramon"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://7c4299fd-a-62cb3a1a-s-sites.googlegroups.com/site/takashiowada54/files/Dissertation_Main.pdf?attachauth=ANoY7cqLrOcqDFe9W9t4nEvuiM-VrXhW8Ko4OqTQ8cuaz9kdklj0ZnCfr8VIkyuL5vK4NxMU_4oTw153ueuTCwH8UpHADQgk9oSsrUyVWhhAagl7C2G0HandV-BxFBRniS3_543BGbeNYy8tOarMDnFgBBKIZnXdgIB66lWU9_6hzIpvVWmVgnkSAbFvNkzDF1GPhi4MuY2pL7Icnqv9Nbzakw1nKui0YbXoWHpIeiRurnQyE-I6nwY%3D&amp;attredirects=0">
    <title>ERGODIC THEORETICAL APPROACH TO INVESTIGATE MEMORY PROPERTIES OF HEAVY TAILED PROCESSES</title>
    <dc:date>2016-01-07T02:22:45+00:00</dc:date>
    <link>https://7c4299fd-a-62cb3a1a-s-sites.googlegroups.com/site/takashiowada54/files/Dissertation_Main.pdf?attachauth=ANoY7cqLrOcqDFe9W9t4nEvuiM-VrXhW8Ko4OqTQ8cuaz9kdklj0ZnCfr8VIkyuL5vK4NxMU_4oTw153ueuTCwH8UpHADQgk9oSsrUyVWhhAagl7C2G0HandV-BxFBRniS3_543BGbeNYy8tOarMDnFgBBKIZnXdgIB66lWU9_6hzIpvVWmVgnkSAbFvNkzDF1GPhi4MuY2pL7Icnqv9Nbzakw1nKui0YbXoWHpIeiRurnQyE-I6nwY%3D&amp;attredirects=0</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to:NB stochastic_processes heavy_tails ergodic_theory long-range_dependence re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:18ab9ef7cfc9/</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:heavy_tails"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:long-range_dependence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.maths.manchester.ac.uk/~goran/lectures.pdf">
    <title>From Uniform Laws of Large Numbers to Uniform Ergodic Theorems</title>
    <dc:date>2015-08-27T00:24:46+00:00</dc:date>
    <link>http://www.maths.manchester.ac.uk/~goran/lectures.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The purpose of these lectures is to present three different approaches with their own methods for establishing uniform laws of large numbers and uni- form ergodic theorems for dynamical systems. The presentation follows the principle according to which the i.i.d. case is considered first in great de- tail, and then attempts are made to extend these results to the case of more general dependence structures. The lectures begin (Chapter 1) with a re- view and description of classic laws of large numbers and ergodic theorems, their connection and interplay, and their infinite dimensional extensions to- wards uniform theorems with applications to dynamical systems. The first approach (Chapter 2) is of metric entropy with bracketing which relies upon the Blum-DeHardt law of large numbers and Hoffmann-Jørgensen’s exten- sion of it. The result extends to general dynamical systems using the uniform ergodic lemma (or Kingman’s subadditive ergodic theorem). In this context metric entropy and majorizing measure type conditions are also considered. The second approach (Chapter 3) is of Vapnik and Chervonenkis. It relies upon Rademacher randomization (subgaussian inequality) and Gaussian ran- domization (Sudakov’s minoration) and offers conditions in terms of random entropy numbers. Absolutely regular dynamical systems are shown to sup- port the VC theory using a blocking technique and Eberlein’s lemma. The third approach (Chapter 4) is aimed to cover the wide sense stationary case which is not accessible by the previous two methods. This approach relies upon the spectral representation theorem and offers conditions in terms of the orthogonal stochastic measures which are associated with the underlying dynamical system by means of this theorem. The case of bounded variation is covered, while the case of unbounded variation is left as an open question. The lectures finish with a supplement in which the role of uniform conver- gence of reversed martingales towards consistency of statistical models is explained via the concept of Hardy’s regular convergence."

--- I got a glance at this once a decade ago in a library, and have been looking for a copy for years.

---ETA after reading: [http://bactra.org/weblog/algae-2019-05.html#peskir]]]></description>
<dc:subject>in_NB ergodic_theory vc-dimension learning_theory stochastic_processes empirical_processes have_read books:recommended 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:f5f9b778314c/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:vc-dimension"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:recommended"/>
	<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="http://arxiv.org/abs/1505.01163">
    <title>[1505.01163] Stationarity Tests for Time Series -- What Are We Really Testing?</title>
    <dc:date>2015-05-20T19:02:47+00:00</dc:date>
    <link>http://arxiv.org/abs/1505.01163</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Traditionally stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths denoted as A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions. The results justify our intuition about how a "typical" stationary process should look like, and potentially lead to new families of stationarity tests."

--- The "set A" is basically "paths where time averages behave nicely; this is very close to Furstenberg's old book, which they cite at one point but don't really draw out.  It's also close to what some authors call the set of "ergodic points".]]></description>
<dc:subject>time_series ergodic_theory statistics statistical_inference_for_stochastic_processes re:almost_none re:ADAfaEPoV in_NB have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f5a9d997df33/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<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:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://math.caltech.edu/simon/ComprehensiveCoursePreview.html">
    <title>A Comprehensive Course in Analysis - Preview</title>
    <dc:date>2015-01-27T03:52:58+00:00</dc:date>
    <link>http://math.caltech.edu/simon/ComprehensiveCoursePreview.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[To quote Max: WANT.]]></description>
<dc:subject>books:noted analysis mathematics fourier_analysis ergodic_theory to:NB coveted hilbert_space hyperbolic_geometry via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:36f9e8137399/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fourier_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:coveted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hyperbolic_geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.bj/1402488943">
    <title>Dehling , Durieu , Tusche : Approximating class approach for empirical processes of dependent sequences indexed by functions</title>
    <dc:date>2015-01-24T14:13:31+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.bj/1402488943</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study weak convergence of empirical processes of dependent data (Xi)i≥0, indexed by classes of functions. Our results are especially suitable for data arising from dynamical systems and Markov chains, where the central limit theorem for partial sums of observables is commonly derived via the spectral gap technique. We are specifically interested in situations where the index class  is different from the class of functions f for which we have good properties of the observables (f(Xi))i≥0. We introduce a new bracketing number to measure the size of the index class  which fits this setting. Our results apply to the empirical process of data (Xi)i≥0 satisfying a multiple mixing condition. This includes dynamical systems and Markov chains, if the Perron–Frobenius operator or the Markov operator has a spectral gap, but also extends beyond this class, for example, to ergodic torus automorphisms."]]></description>
<dc:subject>empirical_processes approximation stochastic_processes markov_models dynamical_systems ergodic_theory mixing in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b57eb1847383/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<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:dynamical_systems"/>
	<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:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1411.7650">
    <title>[1411.7650] Nonparametric statistical inference for the context tree of a stationary ergodic process</title>
    <dc:date>2015-01-20T04:00:15+00:00</dc:date>
    <link>http://arxiv.org/abs/1411.7650</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the processes. As a starting point we introduce a Hamming metric in the space of irreducible context trees and we use the properties of the weak topology in the space of ergodic stationary processes to prove that if the Hamming metric is unbounded, there exist no consistent estimators for the context tree. Even in the bounded case we show that there exist no two-sided confidence bounds. However we prove that one-sided inference is possible in this general setting and we construct a consistent estimator that is a lower bound for the context tree of the process with an explicit formula for the coverage probability."]]></description>
<dc:subject>statistics statistical_inference_for_stochastic_processes ergodic_theory prediction re:AoS_project confidence_sets variable-length_markov_models_aka_context_trees have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7ff1521daee5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable-length_markov_models_aka_context_trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.cambridge.org/us/academic/subjects/mathematics/abstract-analysis/probability-classical-limit-theorems?format=HB">
    <title>Probability: The Classical Limit Theorems</title>
    <dc:date>2014-10-28T23:24:23+00:00</dc:date>
    <link>http://www.cambridge.org/us/academic/subjects/mathematics/abstract-analysis/probability-classical-limit-theorems?format=HB</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices."]]></description>
<dc:subject>probability books:noted ergodic_theory central_limit_theorem stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8899e7cf990e/</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:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<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:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/math/0305164">
    <title>[math/0305164] Subshifts of quasi-finite type</title>
    <dc:date>2014-09-03T18:41:11+00:00</dc:date>
    <link>http://arxiv.org/abs/math/0305164</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise monotonic maps of the interval with positive entropy. Yet many properties remain: existence of finitely many ergodic invariant probabilities of maximum entropy; lots of periodic points; meromorphic extension of the Artin-Mazur zeta function."]]></description>
<dc:subject>to:NB ergodic_theory symbolic_dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fc07d7f41a92/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1018031110">
    <title>Nobel : Limits to classification and regression estimation from ergodic processes</title>
    <dc:date>2014-08-07T16:06:36+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1018031110</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We answer two open questions concerning the existence of universal schemes for classification and regression estimation from stationary ergodic processes. It is shown that no measurable procedure can produce weakly consistent regression estimates from every bivariate stationary ergodic process, even if the covariate and response variables are restricted to take values in the unit interval. It is further shown that no measurable procedure can produce weakly consistent classification rules from every bivariate stationary ergodic process for which the response variable is binary valued. The results of the paper are derived via reduction arguments and are based in part on recent work concerning density estimaton from ergodic processes."]]></description>
<dc:subject>to_read ergodic_theory classifiers regression learning_theory statistics have_read have_forgotten re:AoS_project nobel.andrew in_NB 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:745ac5dff27e/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:classifiers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<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:have_forgotten"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nobel.andrew"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<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="http://arxiv.org/abs/1406.6670">
    <title>[1406.6670] Learning the ergodic decomposition</title>
    <dc:date>2014-07-12T00:37:22+00:00</dc:date>
    <link>http://arxiv.org/abs/1406.6670</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A Bayesian agent learns about the structure of a stationary process from ob- serving past outcomes. We prove that his predictions about the near future become ap- proximately those he would have made if he knew the long run empirical frequencies of the process."]]></description>
<dc:subject>ergodic_theory statistics time_series statistical_inference_for_stochastic_processes bayesian_consistency in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0f70ca72d21e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<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:bayesian_consistency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1211.0834">
    <title>[1211.0834] On Hidden Markov Processes with Infinite Excess Entropy</title>
    <dc:date>2014-04-28T13:24:08+00:00</dc:date>
    <link>http://arxiv.org/abs/1211.0834</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate stationary hidden Markov processes for which mutual information between the past and the future is infinite. It is assumed that the number of observable states is finite and the number of hidden states is countably infinite. Under this assumption, we show that the block mutual information of a hidden Markov process is upper bounded by a power law determined by the tail index of the hidden state distribution. Moreover, we exhibit three examples of processes. The first example, considered previously, is nonergodic and the mutual information between the blocks is bounded by the logarithm of the block length. The second example is also nonergodic but the mutual information between the blocks obeys a power law. The third example obeys the power law and is ergodic."

Journal version: http://dx.doi.org/10.1007/s10959-012-0468-6]]></description>
<dc:subject>to:NB information_theory ergodic_theory stochastic_processes kith_and_kin debowski.lukasz</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3fdc6dab17a8/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:debowski.lukasz"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1404.0766">
    <title>[1404.0766] Ornstein Isomorphism and Algorithmic Randomness</title>
    <dc:date>2014-04-20T18:27:25+00:00</dc:date>
    <link>http://arxiv.org/abs/1404.0766</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In 1970, Donald Ornstein proved a landmark result in dynamical systems, viz., two Bernoulli systems with the same entropy are isomorphic except for a measure 0 set. Keane and Smorodinsky gave a finitary proof of this result. They also indicated how one can generalize the result to mixing Markov Shifts. We adapt their construction to show that if two computable mixing Markov systems have the same entropy, then there is a layerwise computable isomorphism defined on all Martin-Lof random points in the system. Since the set of Martin-Lof random points forms a measure 1 set, it implies the classical result for such systems.
"This result uses several recent developments in computable analysis and algorithmic randomness. Following the work by Braverman, Nandakumar, and Hoyrup and Rojas introduced discontinuous functions into the study of algorithmic randomness. We utilize Hoyrup and Rojas' elegant notion of layerwise computable functions to produce the test of randomness in our result. Further, we use the recent result of the effective Shannon-McMillan-Breiman theorem, independently established by Hochman and Hoyrup to prove the properties of our construction. 
"We show that the result cannot be improved to include all points in the systems - only trivial computable isomorphisms exist between systems with the same entropy."]]></description>
<dc:subject>ergodic_theory algorithmic_information_theory stochastic_processes to_read entableted in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:77554d37a74e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algorithmic_information_theory"/>
	<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:entableted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.cambridge.org/us/academic/subjects/statistics-probability/applied-probability-and-stochastic-networks/ergodic-control-diffusion-processes?format=HB">
    <title>Ergodic Control of Diffusion Processes | Applied probability and stochastic networks | Cambridge University Press</title>
    <dc:date>2014-03-27T15:52:31+00:00</dc:date>
    <link>http://www.cambridge.org/us/academic/subjects/statistics-probability/applied-probability-and-stochastic-networks/ergodic-control-diffusion-processes?format=HB</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This comprehensive volume on ergodic control for diffusions highlights intuition alongside technical arguments. A concise account of Markov process theory is followed by a complete development of the fundamental issues and formalisms in control of diffusions. This then leads to a comprehensive treatment of ergodic control, a problem that straddles stochastic control and the ergodic theory of Markov processes. The interplay between the probabilistic and ergodic-theoretic aspects of the problem, notably the asymptotics of empirical measures on one hand, and the analytic aspects leading to a characterization of optimality via the associated Hamilton–Jacobi–Bellman equation on the other, is clearly revealed. The more abstract controlled martingale problem is also presented, in addition to many other related issues and models. Assuming only graduate-level probability and analysis, the authors develop the theory in a manner that makes it accessible to users in applied mathematics, engineering, finance and operations research."

- Relevant to defining risk properly for forecasting?]]></description>
<dc:subject>books:noted stochastic_processes ergodic_theory re:XV_for_mixing in_NB control_theory_and_control_engineering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bde861070652/</dc:identifier>
<taxo:topics><rdf:Bag>	<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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:XV_for_mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1023/A:1021692202530">
    <title>Multivariate Sampling and the Estimation Problem for Exchangeable Arrays - Springer</title>
    <dc:date>2014-03-26T14:10:41+00:00</dc:date>
    <link>http://link.springer.com/article/10.1023/A:1021692202530</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider random arrays and the associated empirical distributions obtained by multivariate sampling from a stationary process. Under suitable conditions, one gets convergence toward a separately exchangeable array and its ergodic distribution. The result is related to the statistical problem of estimating the representing function of an exchangeable array. The latter problem is well-posed only for shell-measurable arrays, where the grid processes based on finite sub-arrays form consistent estimates with respect to a suitable norm. In general, the required consistency holds only in the distributional sense for the generated arrays."]]></description>
<dc:subject>stochastic_processes exchangeability statistical_inference_for_stochastic_processes kallenberg.olav re:smoothing_adjacency_matrices network_data_analysis statistics in_NB have_read ergodic_theory to_teach:graphons exchangeable_arrays</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f9139f894731/</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:exchangeability"/>
	<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:kallenberg.olav"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:smoothing_adjacency_matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:graphons"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exchangeable_arrays"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0707.0322">
    <title>[0707.0322] Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise</title>
    <dc:date>2014-03-12T20:37:56+00:00</dc:date>
    <link>http://arxiv.org/abs/0707.0322</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable α-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of ℝd and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than α-mixing."]]></description>
<dc:subject>dynamical_systems mixing ergodic_theory nonparametrics statistics prediction support-vector_machines steinwart.ingo time_series statistical_inference_for_stochastic_processes re:your_favorite_dsge_sucks re:XV_for_mixing to_read in_NB entableted</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a11e92b7fc51/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:support-vector_machines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:steinwart.ingo"/>
	<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:re:your_favorite_dsge_sucks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:XV_for_mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aop/1393251303">
    <title>Berkes , Liu , Wu : Komlós–Major–Tusnády approximation under dependence</title>
    <dc:date>2014-03-12T19:14:12+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aop/1393251303</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The celebrated results of Komlós, Major and Tusnády [Z. Wahrsch. Verw. Gebiete 32 (1975) 111–131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33–58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a powerful tool in probability and statistics. In this paper we extend KMT approximation for a large class of dependent stationary processes, solving a long standing open problem in probability theory. Under the framework of stationary causal processes and functional dependence measures of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150–14154], we show that, under natural moment conditions, the partial sum processes can be approximated by Wiener process with an optimal rate. Our dependence conditions are mild and easily verifiable. The results are applied to ergodic sums, as well as to nonlinear time series and Volterra processes, an important class of nonlinear processes."]]></description>
<dc:subject>to:NB mixing ergodic_theory convergence_of_stochastic_processes central_limit_theorem stochastic_processes re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e3a22f3fd2d2/</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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convergence_of_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:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1403.1757">
    <title>[1403.1757] Hilberg Exponents: New Measures of Long Memory in the Process</title>
    <dc:date>2014-03-10T17:57:01+00:00</dc:date>
    <link>http://arxiv.org/abs/1403.1757</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper concerns the rates of hyperbolic growth of mutual information computed for a stationary measure or for a universal code. The rates are called Hilberg exponents and four such quantities are defined for each measure and each code: two random exponents and two expected exponents. A particularly interesting case arises for conditional algorithmic mutual information. In this case, the random Hilberg exponents are almost surely constant on ergodic sources and are bounded by the expected Hilberg exponents. This property is a ``second-order'' analogue of the Shannon-McMillan-Breiman theorem, proved without invoking the ergodic theorem. It carries over to Hilberg exponents for the underlying probability measure via Shannon-Fano coding and Barron inequality. Moreover, the expected Hilberg exponents can be linked for different universal codes. Namely, if one code dominates another, the expected Hilberg exponents are greater for the former than for the latter. The paper is concluded by an evaluation of Hilberg exponents for certain sources such as the Bayesian Bernoulli process and the Santa Fe processes."]]></description>
<dc:subject>information_theory ergodic_theory stochastic_processes long-range_dependence to_read debowski.lukasz algorithmic_information_theory kith_and_kin in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9c8a457bf2f1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:long-range_dependence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:debowski.lukasz"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algorithmic_information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.1873">
    <title>[1402.1873] Exact fluctuation theorem without ensemble quantities</title>
    <dc:date>2014-02-11T21:37:24+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.1873</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Evaluating the entropy production (EP) along a stochastic trajectory requires the knowledge of the system probability distribution, an ensemble quantity notoriously difficult to measure. In this letter, we show that the EP of nonautonomous systems in contact with multiple reservoirs can be expressed solely in terms of physical quantities measurable at the single trajectory level with a suitable preparation of the initial condition. As a result, we identify universal energy and particle fluctuation relations valid for any measurement time. We apply our findings to an electronic junction model which may be used to verify our prediction experimentally."]]></description>
<dc:subject>statistical_mechanics non-equilibrium ergodic_theory in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a2fd9144d0ed/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aap/1386857853">
    <title>Bušić , Mairesse , Marcovici : Probabilistic cellular automata, invariant measures, and perfect sampling</title>
    <dc:date>2013-12-16T01:55:56+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aap/1386857853</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. We investigate the ergodicity of this Markov chain. A classical cellular automaton is a particular case of PCA. For a one-dimensional cellular automaton, we prove that ergodicity is equivalent to nilpotency, and is therefore undecidable. We then propose an efficient perfect sampling algorithm for the invariant measure of an ergodic PCA. Our algorithm does not assume any monotonicity property of the local rule. It is based on a bounding process which is shown to also be a PCA. Last, we focus on the PCA majority, whose asymptotic behavior is unknown, and perform numerical experiments using the perfect sampling procedure."

- Really, ergodicity is undecidable?!?]]></description>
<dc:subject>to:NB cellular_automata ergodic_theory stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e4a6b142554f/</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:cellular_automata"/>
	<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="http://arxiv.org/abs/1312.2726">
    <title>[1312.2726] Asymptotic mean stationarity and absolute continuity of point process distributions</title>
    <dc:date>2013-12-11T20:41:36+00:00</dc:date>
    <link>http://arxiv.org/abs/1312.2726</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper relates - for point processes Φ on ℝ - two types of asymptotic mean stationarity (AMS) properties and several absolute continuity results for the common probability measures emerging from point process theory. It is proven that Φ is AMS under the time-shifts if and only if it is AMS under the event-shifts. The consequences for the accompanying two types of ergodic theorem are considered. Furthermore, the AMS properties are equivalent or closely related to several absolute continuity results. Thus, the class of AMS point processes is characterized in several ways. Many results from stationary point process theory are generalized for AMS point processes. To obtain these results, we first use Campbell's equation to rewrite the well-known Palm relationship for general nonstationary point processes into expressions which resemble results from stationary point process theory."]]></description>
<dc:subject>ergodic_theory point_processes stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6369b09d965e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<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:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ndpr.nd.edu/news/43974-tychomancy-inferring-probability-from-causal-structure/">
    <title>Tychomancy: Inferring Probability from Causal Structure // Reviews // Notre Dame Philosophical Reviews // University of Notre Dame</title>
    <dc:date>2013-11-06T18:30:29+00:00</dc:date>
    <link>http://ndpr.nd.edu/news/43974-tychomancy-inferring-probability-from-causal-structure/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Ouch.  Polite, but ouch.]]></description>
<dc:subject>books:noted book_reviews foundations_of_statistics statistical_mechanics probability ergodic_theory philosophy_of_science strevens.michael howson.colin in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:24c7e6751953/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:book_reviews"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:foundations_of_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:philosophy_of_science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:strevens.michael"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:howson.colin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1310.1573">
    <title>[1310.1573] Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems</title>
    <dc:date>2013-10-08T18:23:01+00:00</dc:date>
    <link>http://arxiv.org/abs/1310.1573</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusion are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures."]]></description>
<dc:subject>ergodic_theory statistical_mechanics foundations_of_statistical_mechanics philosophy_of_science in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:34b6a7cf2ed2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:foundations_of_statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:philosophy_of_science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.4859">
    <title>[1309.4859] Predictive PAC Learning and Process Decompositions</title>
    <dc:date>2013-09-20T12:59:20+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.4859</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not decay at the same rate. In this paper, we argue that it is natural in predictive PAC to condition not on the past observations but on the mixture component of the sample path. This definition not only matches what a realistic learner might demand, but also allows us to sidestep several otherwise grave problems in learning from dependent data. In particular, we give a novel PAC generalization bound for mixtures of learnable processes with a generalization error that is not worse than that of each mixture component. We also provide a characterization of mixtures of absolutely regular ($\beta$-mixing) processes, of independent probability-theoretic interest."]]></description>
<dc:subject>self-centered in_NB mixing ergodic_theory stochastic_processes learning_theory mixture_models prediction kontorovich.aryeh</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:761883d720df/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-centered"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixture_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kontorovich.aryeh"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jstor.org/discover/10.2307/2999460?uid=3739864&amp;uid=2129&amp;uid=2&amp;uid=70&amp;uid=4&amp;uid=3739256&amp;sid=21102630678603">
    <title>Bayesian Representations of Stochastic Processes Under Learning: de Finetti Revisited (Jackson, Kalai and Smorodinsky, Econometrica 67 (1999): 875--893)</title>
    <dc:date>2013-09-09T03:34:37+00:00</dc:date>
    <link>http://www.jstor.org/discover/10.2307/2999460?uid=3739864&amp;uid=2129&amp;uid=2&amp;uid=70&amp;uid=4&amp;uid=3739256&amp;sid=21102630678603</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form <tex-math>$\mu =\int_{\Theta}\mu _{\theta }d\lambda (\theta)$</tex-math>. Among these, a natural representation is one whose components <tex-math>$(\mu _{\theta}\text{'}{\rm s})$</tex-math> are "learnable" (one can approximate μ <sub>θ</sub> by conditioning μ on observation of the process) and "sufficient for prediction" (<tex-math>$\mu _{\theta}\text{'}{\rm s}$</tex-math> predictions are not aided by conditioning on observation of the process). We show the existence and uniqueness of such a representation under a suitable asymptotic mixing condition on the process. This representation can be obtained by conditioning on the tail-field of the process, and any learnable representation that is sufficient for prediction is asymptotically like the tail-field representation. This result is related to the celebrated de Finetti theorem, but with exchangeability weakened to an asymptotic mixing condition, and with his conclusion of a decomposition into i.i.d. component distributions weakened to components that are learnable and sufficient for prediction."

- A bit astonishing there's no mention of de-Finetti-like theorems for partial exchangeability, or even of the ergodic decomposition.]]></description>
<dc:subject>stochastic_processes mixing learning_theory re:almost_none jackson.matthew_o. ergodic_theory re:pac-and-mar not_quite_scooped_exactly have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5645e3ec2909/</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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:jackson.matthew_o."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:pac-and-mar"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:not_quite_scooped_exactly"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007/s10955-013-0796-7">
    <title>A Thermodynamic Formalism for Continuous Time Markov Chains with Values on the Bernoulli Space: Entropy, Pressure and Large Deviations - Springer</title>
    <dc:date>2013-09-03T12:24:15+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/s10955-013-0796-7</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice {1,…,d}ℕ (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator , where is a discrete time Ruelle operator (transfer operator), and A:{1,…,d}ℕ→ℝ is a given fixed Lipschitz function. The associated continuous time stationary Markov chain will define the a priori probability.
"Given a Lipschitz interaction V:{1,…,d}ℕ→ℝ , we are interested in Gibbs (equilibrium) state for such V. This will be another continuous time stationary Markov chain. In order to analyze this problem we will use a continuous time Ruelle operator (transfer operator) naturally associated to V. Among other things we will show that a continuous time Perron-Frobenius Theorem is true in the case V is a Lipschitz function.
"We also introduce an entropy, which is negative (see also Lopes et al. in Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature. Arxiv, 2012), and we consider a variational principle of pressure. Finally, we analyze large deviations properties for the empirical measure in the continuous time setting using results by Y. Kifer (Tamsui Oxf. J. Manag. Sci. 321(2):505–524, 1990). In the last appendix of the paper we explain why the techniques we develop here have the capability to be applied to the analysis of convergence of a certain version of the Metropolis algorithm."]]></description>
<dc:subject>to:NB ergodic_theory statistical_mechanics markov_models stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d379ea356a1a/</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:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<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="http://www.nowpublishers.com/articles/foundations-and-trends-in-stochastic-systems/STO-004">
    <title>now publishers – Long Range Dependence</title>
    <dc:date>2013-08-15T15:19:37+00:00</dc:date>
    <link>http://www.nowpublishers.com/articles/foundations-and-trends-in-stochastic-systems/STO-004</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested. A number of related topics is also discussed, including connections with non-stationary processes, with ergodic theory, self-similar processes and fractionally differenced processes, heavy tails and light tails, limit theorems and large deviations."]]></description>
<dc:subject>to:NB long-range_dependence stochastic_processes ergodic_theory mixing to_read large_deviations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dfd6679f032a/</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:long-range_dependence"/>
	<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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bj/1372251145">
    <title>Talata : Divergence rates of Markov order estimators and their application to statistical estimation of stationary ergodic processes</title>
    <dc:date>2013-06-27T15:03:04+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bj/1372251145</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using penalized maximum likelihood (PML). Under some assumptions on the continuity rate and the assumption of non-nullness, a rate of convergence in d¯-distance is obtained, with explicit constants. The result requires an analysis of the divergence of PML Markov order estimators for not necessarily finite memory processes. This divergence problem is investigated in more generality for three information criteria: the Bayesian information criterion with generalized penalty term yielding the PML, and the normalized maximum likelihood and the Krichevsky–Trofimov code lengths. Lower and upper bounds on the estimated order are obtained. The notion of consistent Markov order estimation is generalized for infinite memory processes using the concept of oracle order estimates, and generalized consistency of the PML Markov order estimator is presented."]]></description>
<dc:subject>to:NB markov_models stochastic_processes model_selection prediction statistics ergodic_theory information_criteria statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:232fc8be2fe3/</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:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_criteria"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1306.3925">
    <title>[1306.3925] Recurrence Theorems: a unified account</title>
    <dc:date>2013-06-18T15:37:38+00:00</dc:date>
    <link>http://arxiv.org/abs/1306.3925</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces, and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics."]]></description>
<dc:subject>foundations_of_statistical_mechanics ergodic_theory quantum_mechanics physics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4a2154a08b92/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:foundations_of_statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:quantum_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.6863">
    <title>[1304.6863] Law Of Large Numbers For Random Dynamical Systems</title>
    <dc:date>2013-04-26T15:23:47+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.6863</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of large numbers."]]></description>
<dc:subject>ergodic_theory dynamical_systems stochastic_processes re:almost_none in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:723e0d175d2a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<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:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.5113">
    <title>[1304.5113] A note on weak convergence of the sequential multivariate empirical process under strong mixing</title>
    <dc:date>2013-04-22T17:23:25+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.5113</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing results in the literature that are based on mixing rates depending on the dimension $d$."]]></description>
<dc:subject>to:NB mixing ergodic_theory empirical_processes stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c7b219da085f/</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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.4580">
    <title>[1304.4580] Quenched Invariance Principles via Martingale Approximation</title>
    <dc:date>2013-04-17T13:05:03+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.4580</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the terminology of central limit theorem and its functional form, started at a point. All these results have in common that they are obtained via a martingale approximation in the almost sure sense. We point out several applications of these results to classes of mixing sequences, shift processes, reversible Markov chains, Metropolis Hastings algorithms."]]></description>
<dc:subject>to:NB stochastic_processes central_limit_theorem markov_models ergodic_theory martingales re:almost_none monte_carlo</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7401f9e40441/</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:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<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:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://users.stat.umn.edu/~geyer/mcmc/burn.html">
    <title>Burn-In is Unnecessary</title>
    <dc:date>2013-04-10T22:04:37+00:00</dc:date>
    <link>http://users.stat.umn.edu/~geyer/mcmc/burn.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Hmmm.  Shouldn't one be able to address this as, given that the initial state X_0 comes from a distribution \pi which is not the invariant distribution \rho of the Markov operator, for what b does the empirical distribution of X_{b:n} come closest, on average and in some reasonable metric, to \rho?  The answer presumably depends on how far \pi is from \rho and how rapidly  T mixes.]]></description>
<dc:subject>monte_carlo to_teach:statcomp ergodic_theory markov_models have_read simulation computational_statistics geyer.charles_j.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e865d44ad838/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:statcomp"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<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:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geyer.charles_j."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.2621">
    <title>[1304.2621] Central limit theorems in linear dynamics</title>
    <dc:date>2013-04-10T21:29:11+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.2621</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Given a bounded operator $T$ on a Banach space $X$, we study the existence of a probability measure $\mu$ on $X$ such that, for many functions $f:X\to\mathbb K$, the sequence $(f+\dots+f\circ T^{n-1})/\sqrt n$ converges in distribution to a Gaussian random variable."]]></description>
<dc:subject>to:NB mixing central_limit_theorem ergodic_theory stochastic_processes dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ee98841bea95/</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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>