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    <title>Pinboard (cshalizi)</title>
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    <description>recent bookmarks from cshalizi</description>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2107.04592"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/1903.01608"/>
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  </channel><item rdf:about="https://arxiv.org/abs/2402.14419">
    <title>[2402.14419] On nonparametric estimation of the interaction function in particle system models</title>
    <dc:date>2024-02-27T20:05:01+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.14419</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an analysis of the stochastic and approximation errors associated with both procedures, along with an examination of certain minimax lower bounds. In particular, we show that there is a natural metric under which the corresponding minimax estimation error of the interaction function converges to zero with parametric rate. This result is rather suprising given complexity of the underlying estimation problem and rather large classes of interaction functions for which the above parametric rate holds."]]></description>
<dc:subject>to:NB interacting_particle_systems statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a64b112d1b62/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:interacting_particle_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
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<item rdf:about="https://www.jstor.org/stable/2529945?origin=crossref">
    <title>Stochastic Models of Compartmental Systems on JSTOR</title>
    <dc:date>2023-09-29T16:12:22+00:00</dc:date>
    <link>https://www.jstor.org/stable/2529945?origin=crossref</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper reviews a stochastic approach to compartmental modeling. The need for stochasticity in the model is motivated by two examples, one concerned with vanadium depuration in marine organisms and the other with the thermal resistance of the green sunfish, Lepomis cyanellus. A stochastic formulation is suggested which includes several sources of stochasticity due to some variability among particles in a given experiment and also to some variability between replicates of an experiment. Many different stochastic models of compartmental systems may be obtained from various combinations of these sources of stochasticity, and the mean and autocovariance functions of these models are derived for some one-compartment systems. The mean value functions are shown to be generally tractable forms which may be readily fitted to data; however, even in the case of time-invariant coefficients, the mean functions are often different from the sums of exponential functions given by the deterministic solution. The causal model cannot be identified on the basis of the mean value function alone; however the covariance structure is unique for each of the proposed causal models. The paper also illustrates some basic statistical analysis with these stochastic models. The estimation of parameters by weighted nonlinear least squares is illustrated by fitting some mean functions of these models to data from the previous examples. The procedure may generate RBAN estimators for both of the examples and an asymptotic goodness-of-fit statistic is formulated. The paper concludes with a short summary of promising areas for future research."]]></description>
<dc:subject>in_NB compartment_models time_series statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f6118c9e68cc/</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:compartment_models"/>
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<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.62.1912">
    <title>Phys. Rev. E 62, 1912 (2000) - Symbolic approach for measuring temporal ``irreversibility''</title>
    <dc:date>2023-04-24T21:59:54+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.62.1912</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We describe a symbolic approach for measuring temporal “irreversibility” in time-series measurements. Temporal irreversibility is important because it excludes Gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes. A symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient, robust to noise, and simplifies statistical analysis of confidence limits. We propose a specific algorithm, called “false flipped symbols,” for establishing the presence of temporal irreversibility without the need for generating surrogate data. Besides characterizing experimental data, our results are relevant to the question of selecting alternative models. We illustrate our points with numerical model output and experimental measurements."]]></description>
<dc:subject>time_series statistical_inference_for_stochastic_processes symbolic_dynamics model_checking hypothesis_testing cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 have_read to:NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:405b67266133/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
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<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.51.3871">
    <title>Phys. Rev. E 51, 3871 (1995) - Symbol sequence statistics in noisy chaotic signal reconstruction</title>
    <dc:date>2023-04-24T21:48:32+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.51.3871</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A method is discussed for reconstructing chaotic systems from noisy signals using a symbolic approach. The state space of the dynamical system is partitioned into subregions and a symbol is assigned to each subregion. Consequently, an orbit in a continuous state space is converted into a long symbol string. The probabilities of occurrence for different symbol sequences constitute the symbol sequence statistics. The symbol sequence statistics are easily measured from the signal output and are used as the target for reconstruction (i.e., for assessing the goodness of fit of proposed models). Reliable reconstructions were achieved given a noisy chaotic signal, provided the general class of the model of the underlying dynamics is known. Both observational and dynamical noise were considered, and they were not limited to small amplitudes. Substantial noise produces a strong bias in the symbol sequence statistics, but such bias can be tracked and effectively eliminated by including the noise characteristics in the model. This is demonstrated by the robust reconstruction of the Hénon and Ikeda maps even when the signal to noise ratio is ≊1. Applications of this method include extracting control parameters for nonlinear dynamical systems and nonlinear model evaluation from experimental data."]]></description>
<dc:subject>symbolic_dynamics dynamical_systems time_series statistical_inference_for_stochastic_processes cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 have_read re:dissertation estimation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:04d216b60071/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:dissertation"/>
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<item rdf:about="https://doi.org/10.1016/0022-2496(66)90020-4">
    <title>The structure of responses to a sequence of binary events - ScienceDirect</title>
    <dc:date>2023-04-24T21:43:30+00:00</dc:date>
    <link>https://doi.org/10.1016/0022-2496(66)90020-4</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A procedure developed by Foulkes for determining the structure of a sequence of binary events was found to be a useful base-line model of structure determination by human subjects. The structure is represented in terms of the subsequences of events (states) which lead to different probabilities of the events. While the subjects' behavior after each state is not given by the Foulkes procedure, their behavior appeared to be largely a function of the probabilities of the events after each state (matching) and the lastest event in the state (positive recency)."

--- The Foulkes (1959) paper lying behind this is truly wild as a flash of genius but doesn't seem to be online anywhere.  (I may rectify this.)]]></description>
<dc:subject>have_read markov_models cognitive_science variable-length_markov_models_aka_context_trees statistical_inference_for_stochastic_processes re:AoS_project cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 re:dissertation prediction in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:851a2a33fb27/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
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<item rdf:about="https://www.jstor.org/stable/2336834">
    <title>Parameter-Based Asymptotics on JSTOR</title>
    <dc:date>2023-04-24T21:32:07+00:00</dc:date>
    <link>https://www.jstor.org/stable/2336834</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In certain cases statistical methods based on standard maximum likelihood asymptotics become valid as the true parameter value approaches a boundary of the parameter space. Examples are given which motivate a general parameter-based asymptotic theory, and a result is obtained which covers such situations. Of particular interest are applications to stochastic process models."]]></description>
<dc:subject>to_reread estimation statistics cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 likelihood statistical_inference_for_stochastic_processes re:HEAS in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5c278c6fcc6d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_reread"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:HEAS"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2109.03582">
    <title>[2109.03582] Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes</title>
    <dc:date>2023-02-15T19:57:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.03582</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time. By conditioning the process on its filtration, we introduce a family of higher order kernel mean embeddings (KMEs) that generalizes the notion of KME and captures additional information related to the filtration. We derive empirical estimators for the associated higher order maximum mean discrepancies (MMDs) and prove consistency. We then construct a filtration-sensitive kernel two-sample test able to pick up information that gets missed by the standard MMD test. In addition, leveraging our higher order MMDs we construct a family of universal kernels on stochastic processes that allows to solve real-world calibration and optimal stopping problems in quantitative finance (such as the pricing of American options) via classical kernel-based regression methods. Finally, adapting existing tests for conditional independence to the case of stochastic processes, we design a causal-discovery algorithm to recover the causal graph of structural dependencies among interacting bodies solely from observations of their multidimensional trajectories."

--- ETA after reading: This feels like a strange paper.  I'm not sure I truly understand what theiur "signature statistics" do, nor do I quite get the claimed advantage of higher-order process kernels over "first-order" kernels.  (Proofs are referred to other, older papers.)  And the notion of "causality" between processes seems very weird, since I don't see how it accounts for the flow of time, and of influence, within or across processes, they're being treated like big but indecomposable objects.  Probably should track down references and see if this makes more sense when I put those together.]]></description>
<dc:subject>to:NB stochastic_processes kernel_methods causal_discovery time_series statistical_inference_for_stochastic_processes hilbert_space re:codename:catherine_wheel two-sample_tests statistics have_read path_signatures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:105636bb7bad/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
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</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.jstatsoft.org/article/view/v101i08">
    <title>Inference Tools for Markov Random Fields on Lattices: The R Package mrf2d | Journal of Statistical Software</title>
    <dc:date>2022-06-15T07:49:49+00:00</dc:date>
    <link>https://www.jstatsoft.org/article/view/v101i08</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Markov random fields on two-dimensional lattices are behind many image analysis methodologies. mrf2d provides tools for statistical inference on a class of discrete stationary Markov random field models with pairwise interaction, which includes many of the popular models such as the Potts model and texture image models. The package introduces representations of dependence structures and parameters, visualization functions and efficient (C++-based) implementations of sampling algorithms, common estimation methods and other key features of the model, providing a useful framework to implement algorithms and working with the model in general. This paper presents a description and details of the package, as well as some reproducible examples of usage."]]></description>
<dc:subject>to:NB random_fields monte_carlo R statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1a0c75188ebb/</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:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:R"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s11203-021-09266-0">
    <title>Quasi-likelihood analysis and its applications | SpringerLink</title>
    <dc:date>2022-05-11T17:21:09+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s11203-021-09266-0</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Ibragimov–Khasminskii theory established a scheme that gives asymptotic properties of the likelihood estimators through the convergence of the likelihood ratio random field. This scheme is extending to various nonlinear stochastic processes, combined with a polynomial type large deviation inequality proved for a general locally asymptotically quadratic quasi-likelihood random field. We give an overview of the quasi-likelihood analysis and its applications to ergodic/non-ergodic statistics for stochastic processes."]]></description>
<dc:subject>to:NB likelihood statistical_inference_for_stochastic_processes large_deviations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:658283b0ff7e/</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:likelihood"/>
	<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:large_deviations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://bactra.org/weblog/raffle.html">
    <title>Random-Feature Matching</title>
    <dc:date>2021-11-18T03:53:22+00:00</dc:date>
    <link>http://bactra.org/weblog/raffle.html</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>simulation-based_inference random_features self-promotion statistical_inference_for_stochastic_processes re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:393a9631b8b8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:simulation-based_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_features"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-promotion"/>
	<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:codename:catherine_wheel"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.04592">
    <title>[2107.04592] Statistical Estimation and Nonlinear Filtering in Environmental Pollution</title>
    <dc:date>2021-07-12T15:33:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.04592</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly consistent estimators of the parameters are derived at first. With the optimal filter given by Bayes formula, the uniqueness of invariant measure for the signal-filter pair has been verified. The paper then establishes approximation to the optimal filter, showing that the pathwise average distance, per unit time, of the computed approximating filter from the optimal filter converges to zero in probability. Simulation results are presented at last."]]></description>
<dc:subject>to:NB state_estimation statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fbdbd601df1f/</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:state_estimation"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.09045">
    <title>[2101.09045] Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media</title>
    <dc:date>2021-07-01T13:29:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.09045</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The inference of Markov models from data on stochastic dynamical trajectories over the large time-window T is revisited via the Large Deviations at Level 2.5 for the time-empirical density and the time-empirical flows. The goal is to obtain the large deviations properties for the probability distribution of the inferred Markov parameters in order to characterize their possible fluctuations around the true Markov parameters for large T. The explicit rate functions are given for several settings, namely discrete-time Markov chains, continuous-time Markov jump processes, and diffusion processes in dimension d. Applications to various models of random walks in disordered media are described, where the goal is to infer the quenched disordered variables defining a given disordered sample."]]></description>
<dc:subject>to:NB markov_models large_deviations statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f99b5b88b07a/</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:large_deviations"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.12936">
    <title>[2106.12936] Fundamental limits for learning hidden Markov model parameters</title>
    <dc:date>2021-06-25T15:09:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.12936</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the frontier between learnable and unlearnable hidden Markov models (HMMs). HMMs are flexible tools for clustering dependent data coming from unknown populations. The model parameters are known to be identifiable as soon as the clusters are distinct and the hidden chain is ergodic with a full rank transition matrix. In the limit as any one of these conditions fails, it becomes impossible to identify parameters. For a chain with two hidden states we prove nonasymptotic minimax upper and lower bounds, matching up to constants, which exhibit thresholds at which the parameters become learnable."]]></description>
<dc:subject>to:NB state-space_models minimax statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8c037ff7a877/</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:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:minimax"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.12064">
    <title>[2106.12064] Assessing epidemic curves for evidence of superspreading</title>
    <dc:date>2021-06-25T15:08:38+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.12064</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The expected number of secondary infections arising from each index case, the reproduction number, or R number is a vital summary statistic for understanding and managing epidemic diseases. There are many methods for estimating R; however, few of these explicitly model heterogeneous disease reproduction, which gives rise to superspreading within the population. Here we propose a parsimonious discrete-time branching process model for epidemic curves that incorporates heterogeneous individual reproduction numbers. Our Bayesian approach to inference illustrates that this heterogeneity results in less certainty on estimates of the time-varying cohort reproduction number Rt. Leave-future-out cross-validation evaluates the predictive performance of the proposed model, allowing us to assess epidemic curves for evidence of superspreading. We apply these methods to a COVID-19 epidemic curve for the Republic of Ireland and find some support for heterogeneous disease reproduction. We conclude that the 10\% most infectious index cases account for approximately 40-80\% of the expected secondary infections. Our analysis highlights the difficulties in identifying heterogeneous disease reproduction from epidemic curves and that heterogeneity is a vital consideration when estimating Rt."]]></description>
<dc:subject>to:NB epidemiology branching_processes statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3ffae71efc21/</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:epidemiology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:branching_processes"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.00308">
    <title>[2011.00308] Mixing it up: A general framework for Markovian statistics</title>
    <dc:date>2021-06-25T14:55:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.00308</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of estimators for the characteristics of the process in the minimax sense, it restricts the applicability of results to a rather constrained set of stochastic processes and in particular hardly allows incorporating jump structures. As a consequence, for many models of applied and theoretical interest, no statement can be made about the robustness of typical statistical procedures beyond the beautiful, but limited framework available in the literature. To close this gap, we identify β-mixing of the process and heat kernel bounds on the transition density as a suitable combination to obtain sup-norm and L2 kernel invariant density estimation rates matching the case of reversible multidimenisonal diffusion processes and outperforming density estimation based on discrete i.i.d. or weakly dependent data. Moreover, we demonstrate how up to log-terms, optimal sup-norm adaptive invariant density estimation can be achieved within our general framework based on tight uniform moment bounds and deviation inequalities for empirical processes associated to additive functionals of Markov processes. The underlying assumptions are verifiable with classical tools from stability theory of continuous time Markov processes and PDE techniques, which opens the door to evaluate statistical performance for a vast amount of Markov models. We highlight this point by showing how multidimensional jump SDEs with Lévy driven jump part under different coefficient assumptions can be seamlessly integrated into our framework, thus establishing novel adaptive sup-norm estimation rates for this class of processes."]]></description>
<dc:subject>to:NB to_read markov_models minimax empirical_processes statistical_inference_for_stochastic_processes re:almost_none mixing statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:60fea291f30b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:minimax"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<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:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.05201">
    <title>General-order observation-driven models: ergodicity and consistency of the maximum likelihood estimator</title>
    <dc:date>2021-06-10T02:15:01+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.05201</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The class of observation-driven models (ODMs) includes many models of non-linear time series which, in a fashion similar to, yet different from, hidden Markov models (HMMs), involve hidden variables. Interestingly, in contrast to most HMMs, ODMs enjoy likelihoods that can be computed exactly with computational complexity of the same order as the number of observations, making maximum likelihood estimation the privileged approach for statistical inference for these models. A celebrated example of general order ODMs is the GARCH(p,q) model, for which ergodicity and inference has been studied extensively. However little is known on more general models, in particular integer-valued ones, such as the log-linear Poisson GARCH or the NBIN-GARCH of order (p,q) about which most of the existing results seem restricted to the case p=q=1. Here we fill this gap and derive ergodicity conditions for general ODMs. The consistency and the asymptotic normality of the maximum likelihood estimator (MLE) can then be derived using the method already developed for first order ODMs."]]></description>
<dc:subject>to:NB douc.randal statistical_inference_for_stochastic_processes chains_with_complete_connections time_series statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ef98218f412d/</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:douc.randal"/>
	<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:chains_with_complete_connections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.02735">
    <title>[2106.02735] Data-driven discovery of interacting particle systems using Gaussian processes</title>
    <dc:date>2021-06-08T13:53:49+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.02735</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Interacting particle or agent systems that display a rich variety of collection motions are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and collective behaviors. In this paper, we study the data-driven discovery of distance-based interaction laws in second-order interacting particle systems. We propose a learning approach that models the latent interaction kernel functions as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of interaction kernel function with the pointwise uncertainty quantification, and the other one is the inference of unknown parameters in the non-collective forces of the system. We formulate learning interaction kernel functions as a statistical inverse problem and provide a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. We provide a finite-sample analysis, showing that our posterior mean estimator converges at an optimal rate equal to the one in the classical 1-dimensional Kernel Ridge regression. Numerical results on systems that exhibit different collective behaviors demonstrate efficient learning of our approach from scarce noisy trajectory data."]]></description>
<dc:subject>interacting_particle_systems statistical_inference_for_stochastic_processes equations_of_motion_from_a_time_series in_NB statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e173d059d86c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:interacting_particle_systems"/>
	<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:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.14394">
    <title>[2105.14394] Asymptotic Normality of the Posterior Distributions in a Class of Hidden Markov Models</title>
    <dc:date>2021-06-01T13:33:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.14394</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We show that the posterior distribution of parameters in a hidden Markov model with parametric emission distributions and discrete and known state space is asymptotically normal. The main novelty of our proof is that it is based on a testing condition and the sequence of test functions is obtained using an optimal transportation inequality."]]></description>
<dc:subject>to:NB bayesian_consistency state-space_models statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:63324b05df3f/</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:state-space_models"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2007.08054">
    <title>[2007.08054] Non-parametric estimation of Stochastic Differential Equations from stationary time-series</title>
    <dc:date>2021-05-26T15:56:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.08054</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is motivated by the definition of drift and diffusion coefficients. These estimators involve time- and space-discretization parameters for computing expected values from discretely-sampled stationary data. Next, we analyze consistency and mean squared error of these estimators depending on computational parameters. We derive relationships between the number of observational points, time- and space-discretization parameters in order to achieve the optimal speed of convergence and minimize computational complexity. We illustrate our approach with numerical simulations."]]></description>
<dc:subject>to:NB statistical_inference_for_stochastic_processes stochastic_differential_equations equations_of_motion_from_a_time_series statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:90e586c138c0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2002.07261">
    <title>[2002.07261] Estimating processes in adapted Wasserstein distance</title>
    <dc:date>2021-05-18T13:58:47+00:00</dc:date>
    <link>https://arxiv.org/abs/2002.07261</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and connections to various areas (e.g. Plug-Pichler - stochastic programming, Hellwig - game theory, Aldous - stability of optimal stopping, Hoover-Keisler - model theory). Remarkably, all these seemingly independent approaches define the same adapted weak topology in finite discrete time. Our first main result is to construct an adapted variant of the empirical measure that consistently estimates the laws of stochastic processes in full generality. A natural compatible metric for the weak adapted topology is the given by an adapted refinement of the Wasserstein distance, as established in the seminal works of Pflug-Pichler. Specifically, the adapted Wasserstein distance allows to control the error in stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. in a Lipschitz fashion. The second main result of this article yields quantitative bounds for the convergence of the adapted empirical measure with respect to adapted Wasserstein distance. Surprisingly, we obtain virtually the same optimal rates and concentration results that are known for the classical empirical measure wrt. Wasserstein distance"]]></description>
<dc:subject>to:NB to_read probability stochastic_processes statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a03061cffd40/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<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/2105.04912">
    <title>[2105.04912] On Unbiased Score Estimation for Partially Observed Diffusions</title>
    <dc:date>2021-05-12T18:31:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.04912</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the gradient of the log-likelihood function with respect to parameters, with no time-discretization bias. These estimators can be straightforwardly employed within stochastic gradient methods to perform maximum likelihood estimation or Bayesian inference. As our proposed methodology only requires access to a time-discretization scheme such as the Euler-Maruyama method, it is applicable to a wide class of diffusion processes and observation models. Our approach is based on a representation of the score as a smoothing expectation using Girsanov theorem, and a novel adaptation of the randomization schemes developed in Mcleish [2011], Rhee and Glynn [2015], Jacob et al. [2020a]. This allows one to remove the time-discretization bias and burn-in bias when computing smoothing expectations using the conditional particle filter of Andrieu et al. [2010]. Central to our approach is the development of new couplings of multiple conditional particle filters. We prove under assumptions that our estimators are unbiased and have finite variance. The methodology is illustrated on several challenging applications from population ecology and neuroscience."]]></description>
<dc:subject>to:NB statistical_inference_for_stochastic_processes state-space_models stochastic_differential_equations filtering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b23596cf3c5c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.04390">
    <title>[2105.04390] Statistical inference for continuous-time locally stationary processes using stationary approximations</title>
    <dc:date>2021-05-12T18:16:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.04390</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We establish asymptotic properties of M-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, θ-weak dependence, and hereditary properties, we give sufficient conditions on the contrast function that ensure consistency and asymptotic normality of the M-estimator. As an example, we obtain consistency and asymptotic normality of a localized least squares estimator for observations from a sequence of time-varying Lévy-driven Ornstein-Uhlenbeck processes. Furthermore, for a sequence of time-varying Lévy-driven state space models, we show consistency of a localized Whittle estimator and an M-estimator that is based on a quasi maximum likelihood contrast. Simulation studies show the applicability of the estimation procedures."]]></description>
<dc:subject>to:NB estimation time_series statistics non-stationarity statistical_inference_for_stochastic_processes re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:df61a132f071/</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:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<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:codename:catherine_wheel"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.042310">
    <title>Phys. Rev. E 103, 042310 (2021) - Learning physically consistent differential equation models from data using group sparsity</title>
    <dc:date>2021-04-14T14:43:26+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.042310</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn biologically plausible and physically consistent models rather than models that simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling."]]></description>
<dc:subject>statistical_inference_for_stochastic_processes equations_of_motion_from_a_time_series sparsity in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e7bbb81e3bd3/</dc:identifier>
<taxo:topics><rdf:Bag>	<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:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/content/118/15/e2020397118">
    <title>Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes | PNAS</title>
    <dc:date>2021-04-14T14:28:26+00:00</dc:date>
    <link>https://www.pnas.org/content/118/15/e2020397118</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs), using noisy and sparse data, is a vital task in many fields. We propose a fast and accurate method, manifold-constrained Gaussian process inference (MAGI), for this task. MAGI uses a Gaussian process model over time series data, explicitly conditioned on the manifold constraint that derivatives of the Gaussian process must satisfy the ODE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. MAGI is also suitable for inference with unobserved system components, which often occur in real experiments. MAGI is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which incorporates the ODE system through the manifold constraint. We demonstrate the accuracy and speed of MAGI using realistic examples based on physical experiments."]]></description>
<dc:subject>to:NB statistical_inference_for_stochastic_processes equations_of_motion_from_a_time_series to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:27ddf268fab0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://jmlr.org/papers/v22/19-861.html">
    <title>Learning interaction kernels in heterogeneous systems of agents from multiple trajectories</title>
    <dc:date>2021-04-10T04:24:07+00:00</dc:date>
    <link>https://jmlr.org/papers/v22/19-861.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Systems of interacting particles, or agents, have wide applications in many disciplines, including Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct an estimator based on the minimization of a suitably regularized least squares functional, that is guaranteed to converge, in a suitable L2L2 space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm to construct such estimator, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-prey and swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and can produce accurate predictions of trajectories in large time intervals, even when they are learned from observations in short time intervals."]]></description>
<dc:subject>to:NB agent-based_models interacting_particle_systems statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6cd664197918/</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:agent-based_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:interacting_particle_systems"/>
	<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/2103.05299">
    <title>[2103.05299] Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition</title>
    <dc:date>2021-04-05T21:14:38+00:00</dc:date>
    <link>https://arxiv.org/abs/2103.05299</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we present a maximum likelihood method for estimating the parameters of a univariate Hawkes process with self-excitation or inhibition. Our work generalizes techniques and results that were restricted to the self-exciting scenario. The proposed estimator is implemented for the classical exponential kernel and we show that, in the inhibition context, our procedure provides more accurate estimations than current alternative approaches."]]></description>
<dc:subject>to:NB point_processes statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2a57f65f092c/</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:point_processes"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2003.13555">
    <title>[2003.13555] Causal Inference with Spatio-temporal Data: Estimating the Effects of Airstrikes on Insurgent Violence in Iraq</title>
    <dc:date>2021-03-18T04:51:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2003.13555</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many causal processes have spatial and temporal dimensions. Yet the classic causal inference framework is not directly applicable when the treatment and outcome variables are generated by spatio-temporal processes with an infinite number of possible event locations at each point in time. We take up the challenge of extending the potential outcomes framework to these settings by formulating the treatment point process as stochastic intervention. Our causal estimands include the expected number of outcome events in a specified area of interest under a particular stochastic treatment assignment strategy. We develop an estimation technique that applies the inverse probability of treatment weighting method to spatially-smoothed outcome surfaces. We demonstrate that the proposed estimator is consistent and asymptotically normal as the number of time period approaches infinity. A primary advantage of our methodology is its ability to avoid structural assumptions about spatial spillover and temporal carryover effects. We use the proposed methods to estimate the effects of American airstrikes on insurgent violence in Iraq (February 2007-July 2008). We find that increasing the average number of daily airstrikes for up to one month increases insurgent attacks across Iraq and within Baghdad. We also find evidence that airstrikes can displace attacks from Baghdad to new locations up to 400 kilometers away."]]></description>
<dc:subject>to:NB causal_inference spatio-temporal_statistics point_processes statistical_inference_for_stochastic_processes us-iraq_war statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7b98beae7381/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:point_processes"/>
	<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:us-iraq_war"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.04771">
    <title>[2101.04771] Full-Information Estimation of Heterogeneous Agent Models Using Macro and Micro Data</title>
    <dc:date>2021-01-14T16:19:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.04771</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop a generally applicable full-information inference method for heterogeneous agent models, combining aggregate time series data and repeated cross sections of micro data. To handle unobserved aggregate state variables that affect cross-sectional distributions, we compute a numerically unbiased estimate of the model-implied likelihood function. Employing the likelihood estimate in a Markov Chain Monte Carlo algorithm, we obtain fully efficient and valid Bayesian inference. Evaluation of the micro part of the likelihood lends itself naturally to parallel computing. Numerical illustrations in models with heterogeneous households or firms demonstrate that the proposed full-information method substantially sharpens inference relative to using only macro data, and for some parameters micro data is essential for identification."]]></description>
<dc:subject>agent-based_models statistical_inference_for_stochastic_processes likelihood re:codename:catherine_wheel in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f4bad736b775/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:agent-based_models"/>
	<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:likelihood"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.03562">
    <title>[2101.03562] Bootstrapping Non-Stationary Stochastic Volatility</title>
    <dc:date>2021-01-12T22:40:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.03562</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated volatility processes as well as near-integrated GARCH processes. This paper develops conditions for bootstrap validity in time series regressions with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proving bootstrap validity, involving weak convergence in probability of the bootstrap statistic, fail to deliver the required results. Instead, we use the concept of `weak convergence in distribution' to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change and testing for an autoregressive unit root. Sufficient conditions for bootstrap validity include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results are illustrated using Monte Carlo simulations, which indicate that the wild bootstrap leads to size control even in small samples."]]></description>
<dc:subject>to:NB bootstrap non-stationarity time_series statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f290a00d25d5/</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:bootstrap"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<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:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12582?campaign=wolacceptedarticle">
    <title>Indirect Inference for Time Series Using the Empirical Characteristic Function and Control Variates - Davis - - Journal of Time Series Analysis - Wiley Online Library</title>
    <dc:date>2021-01-10T19:41:39+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12582?campaign=wolacceptedarticle</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We estimate the parameter of a stationary time series process by minimizing the integrated weighted mean squared error between the empirical and simulated characteristic function, when the true characteristic functions cannot be explicitly computed. Motivated by Indirect Inference, we use a Monte Carlo approximation of the characteristic function based on iid simulated blocks. As a classical variance reduction technique, we propose the use of control variates for reducing the variance of this Monte Carlo approximation. These two approximations yield two new estimators that are applicable to a large class of time series processes. We show consistency and asymptotic normality of the parameter estimators under strong mixing, moment conditions, and smoothness of the simulated blocks with respect to its parameter. In a simulation study we show the good performance of these new simulation based estimators, and the superiority of the control variates based estimator for Poisson driven time series of counts."]]></description>
<dc:subject>to:NB indirect_inference time_series statistical_inference_for_stochastic_processes re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b9d051ae1696/</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:indirect_inference"/>
	<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:codename:catherine_wheel"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.14944">
    <title>[2012.14944] Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories</title>
    <dc:date>2021-01-03T19:51:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.14944</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system's dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain."]]></description>
<dc:subject>to:NB stochastic_differential_equations statistical_inference_for_stochastic_processes non-stationarity equations_of_motion_from_a_time_series</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5295ffa6cbe9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-statistics-061120-034438">
    <title>Simulation and Analysis Methods for Stochastic Compartmental Epidemic Models | Annual Review of Statistics and Its Application</title>
    <dc:date>2020-12-18T18:46:24+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-statistics-061120-034438</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article considers simulation and analysis of incidence data using stochastic compartmental models in well-mixed populations. Several simulation approaches are described and compared. Thereafter, we provide an overview of likelihood estimation for stochastic models. We apply one such method to a real-life outbreak data set and compare models assuming different kinds of stochasticity. We also give references for other publications where detailed information on this topic can be found."]]></description>
<dc:subject>to:NB epidemic_models statistical_inference_for_stochastic_processes statistics to_teach:data_over_space_and_time</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d89aa3acdce6/</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:epidemic_models"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.09141">
    <title>[2012.09141] Change Detection: A functional analysis perspective</title>
    <dc:date>2020-12-17T15:28:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.09141</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop a new approach for detecting changes in the behavior of stochastic processes and random fields based on tensor product representations such as the Karhunen-Loève expansion. From the associated eigenspaces of the covariance operator a series of nested function spaces are constructed, allowing detection of signals lying in orthogonal subspaces. In particular this can succeed even if the stochastic behavior of the signal changes either in a global or local sense. A mathematical approach is developed to locate and measure sizes of extraneous components based on construction of multilevel nested subspaces. We show examples in ℝ and on a spherical domain 𝕊2. However, the method is flexible, allowing the detection of orthogonal signals on general topologies, including spatio-temporal domains."]]></description>
<dc:subject>to:NB change-point_problem anomaly_detection principal_components stochastic_processes statistical_inference_for_stochastic_processes statistics spatio-temporal_statistics spatial_statistics time_series hilbert_space</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:20d5ce90dc91/</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:change-point_problem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:anomaly_detection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.06391">
    <title>[2012.06391] Learning physically consistent mathematical models from data using group sparsity</title>
    <dc:date>2020-12-15T01:36:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.06391</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a statistical learning framework based on group-sparse regression that can be used to 1) enforce conservation laws, 2) ensure model equivalence, and 3) guarantee symmetries when learning or inferring differential-equation models from measurement data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas like biology, high noise levels, sensor-induced correlations, and strong inter-system variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn "biologically plausible and physically consistent" models rather than models that simply fit the data best. We present a novel group Iterative Hard Thresholding (gIHT) algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling."]]></description>
<dc:subject>to:NB dynamical_systems statistical_inference_for_stochastic_processes sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7760c0b795d9/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</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://arxiv.org/abs/2012.05601">
    <title>[2012.05601] Bayes posterior convergence for loss functions via almost additive Thermodynamic Formalism</title>
    <dc:date>2020-12-12T20:01:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.05601</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical systems from ergodic observations, where the Bayesian procedure is based on the Gibbs posterior inference, a decision process generalization of standard Bayesian inference where the likelihood is replaced by the exponential of a loss function. In the case of direct observation and almost-additive loss functions, we prove an exponential convergence of the a posteriori measures a limit measure. Our estimates on the Bayes posterior convergence for direct observation are related but complementary to those in a recent paper by K. McGoff, S. Mukherjee and A. Nobel. Our approach makes use of non-additive thermodynamic formalism and large deviation properties instead of joinings."]]></description>
<dc:subject>to:NB bayesian_consistency dynamical_systems statistical_inference_for_stochastic_processes large_deviations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ca38875160c1/</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:dynamical_systems"/>
	<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:large_deviations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2004.09370">
    <title>[2004.09370] Learning Ising models from one or multiple samples</title>
    <dc:date>2020-12-12T19:59:01+00:00</dc:date>
    <link>https://arxiv.org/abs/2004.09370</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["There have been two separate lines of work on estimating Ising models: (1) estimating them from multiple independent samples under minimal assumptions about the model's interaction matrix; and (2) estimating them from one sample in restrictive settings. We propose a unified framework that smoothly interpolates between these two settings, enabling significantly richer estimation guarantees from one, a few, or many samples.
"Our main theorem provides guarantees for one-sample estimation, quantifying the estimation error in terms of the metric entropy of a family of interaction matrices. As corollaries of our main theorem, we derive bounds when the model's interaction matrix is a (sparse) linear combination of known matrices, or it belongs to a finite set, or to a high-dimensional manifold. In fact, our main result handles multiple independent samples by viewing them as one sample from a larger model, and can be used to derive estimation bounds that are qualitatively similar to those obtained in the afore-described multiple-sample literature. Our technical approach benefits from sparsifying a model's interaction network, conditioning on subsets of variables that make the dependencies in the resulting conditional distribution sufficiently weak. We use this sparsification technique to prove strong concentration and anti-concentration results for the Ising model, which we believe have applications beyond the scope of this paper."]]></description>
<dc:subject>to:NB ising_model random_fields statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e567bce5885c/</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:ising_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aos/1607677244">
    <title>Sanders , Proutière , Yun : Clustering in Block Markov Chains</title>
    <dc:date>2020-12-11T17:26:24+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aos/1607677244</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the nn possible states are divided into a finite number of KK groups or clusters, such that states in the same cluster exhibit the same transition rates to other states. One observes a trajectory of the Markov chain, and the objective is to recover, from this observation only, the (initially unknown) clusters. In this paper, we devise a clustering procedure that accurately, efficiently and provably detects the clusters. We first derive a fundamental information-theoretical lower bound on the detection error rate satisfied under any clustering algorithm. This bound identifies the parameters of the BMC, and trajectory lengths, for which it is possible to accurately detect the clusters. We next develop two clustering algorithms that can together accurately recover the cluster structure from the shortest possible trajectories, whenever the parameters allow detection. These algorithms thus reach the fundamental detectability limit, and are optimal in that sense."]]></description>
<dc:subject>to:NB markov_models statistical_inference_for_stochastic_processes clustering statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7c12332b27bd/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:clustering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12573">
    <title>Quasi‐Maximum Likelihood and The Kernel Block Bootstrap for Nonlinear Dynamic Models - Parente - - Journal of Time Series Analysis - Wiley Online Library</title>
    <dc:date>2020-11-30T06:16:20+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12573</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper applies a novel bootstrap method, the kernel block bootstrap, to quasi‐maximum likelihood estimation of dynamic models with stationary strong mixing data. The method first kernel weights the components comprising the quasi‐log likelihood function in an appropriate way and then samples the resultant transformed components using the standard “m out of n" bootstrap. We investigate the first order asymptotic properties of the kernel block bootstrap method for quasi‐maximum likelihood demonstrating, in particular, its consistency and the first‐order asymptotic validity of the bootstrap approximation to the distribution of the quasi‐maximum likelihood estimator. A set of simulation experiments for the mean regression model illustrates the efficacy of the kernel block bootstrap for quasi‐maximum likelihood estimation."]]></description>
<dc:subject>to:NB bootstrap time_series statistical_inference_for_stochastic_processes likelihood statistics kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fd258f2ba0b0/</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:bootstrap"/>
	<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:likelihood"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1907.00113">
    <title>[1907.00113] Learning Markov models via low-rank optimization</title>
    <dc:date>2020-11-30T03:59:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1907.00113</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite of having a large state space, meaning that the system admits a low-dimensional latent structure. We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states. We propose two maximum likelihood estimation methods: a convex approach with nuclear-norm regularization and a nonconvex approach with rank constraint. We explicitly derive the statistical rates of both estimators in terms of the Kullback-Leiber divergence and the ℓ2 error and also establish a minimax lower bound to assess the tightness of these rates. For computing the nonconvex estimator, we develop a novel DC (difference of convex function) programming algorithm that starts with the convex M-estimator and then successively refines the solution till convergence. Empirical experiments demonstrate consistent superiority of the nonconvex estimator over the convex one."

--- Couldn't this be accomplished more simply by using the results about parameterized Markov chains in Billingsley (1961)?  (I guess Billingsley didn't worry about actually finding the optimum.)]]></description>
<dc:subject>to:NB low-rank_approximation markov_models statistics optimization statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7c5dd99517e8/</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:low-rank_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.bj/1605841254">
    <title>Wolfer , Kontorovich : Statistical estimation of ergodic Markov chain kernel over discrete state space</title>
    <dc:date>2020-11-20T04:03:29+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.bj/1605841254</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax sample complexity of estimation with respect to the operator infinity norm, while in the countably infinite case, we analyze the problem with respect to a natural entry-wise norm derived from total variation. We show that in both cases, the sample complexity is governed by the mixing properties of the unknown chain, for which, in the finite-state case, there are known finite-sample estimators with fully empirical confidence intervals."]]></description>
<dc:subject>to:NB markov_models statistical_inference_for_stochastic_processes kith_and_kin kontorovich.aryeh</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3b6d2a8bf1e0/</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:statistical_inference_for_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:kontorovich.aryeh"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aos/1594972822">
    <title>Nickl , Ray : Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions</title>
    <dc:date>2020-11-18T21:47:49+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aos/1594972822</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The problem of determining a periodic Lipschitz vector field b=(b1,…,bd)b=(b1,…,bd) from an observed trajectory of the solution (Xt:0≤t≤T)(Xt:0≤t≤T) of the multi-dimensional stochastic differential equation
dXt=b(Xt)dt+dWt,t≥0,
dXt=b(Xt)dt+dWt,t≥0,
where WtWt is a standard dd-dimensional Brownian motion, is considered. Convergence rates of a penalised least squares estimator, which equals the maximum a posteriori (MAP) estimate corresponding to a high-dimensional Gaussian product prior, are derived. These results are deduced from corresponding contraction rates for the associated posterior distributions. The rates obtained are optimal up to log-factors in L2L2-loss in any dimension, and also for supremum norm loss when d≤4d≤4. Further, when d≤3d≤3, nonparametric Bernstein–von Mises theorems are proved for the posterior distributions of bb. From this, we deduce functional central limit theorems for the implied estimators of the invariant measure μbμb. The limiting Gaussian process distributions have a covariance structure that is asymptotically optimal from an information-theoretic point of view."]]></description>
<dc:subject>to:NB stochastic_differential_equations nonparametrics statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c8f20a18002d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://doi.org/10.1111/sjos.12474">
    <title>Schwartz‐type model selection for ergodic stochastic differential equation models - Eguchi - - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2020-11-15T20:52:34+00:00</dc:date>
    <link>https://doi.org/10.1111/sjos.12474</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study theoretical foundation of model comparison for ergodic stochastic differential equation (SDE) models and an extension of the applicable scope of the conventional Bayesian information criterion. Different from previous studies, we suppose that the candidate models are possibly misspecified models, and we consider both Wiener and a pure‐jump Lévy noise‐driven SDE. Based on the asymptotic behavior of the marginal quasi‐log likelihood, the Schwarz‐type statistics and stepwise model selection procedure are proposed. We also prove the model selection consistency of the proposed statistics with respect to an optimal model. We conduct some numerical experiments and they support our theoretical findings."]]></description>
<dc:subject>to:NB stochastic_differential_equations statistical_inference_for_stochastic_processes information_criteria model_selection</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:906cb1d004b3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_criteria"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.021009">
    <title>Phys. Rev. X 10, 021009 (2020) - Learning Force Fields from Stochastic Trajectories</title>
    <dc:date>2020-07-13T18:05:16+00:00</dc:date>
    <link>https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.021009</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic bound, the capacity of the system when viewed as a communication channel, that limits the rate at which information about the force field can be extracted from a Brownian trajectory. This capacity provides an upper bound to the system’s entropy production rate and quantifies the rate at which the trajectory becomes distinguishable from pure Brownian motion. We propose a practical and principled method, stochastic force inference, that uses this information to approximate force fields and spatially variable diffusion coefficients. It is data efficient, including in high dimensions, robust to experimental noise, and provides a self-consistent estimate of the inference error. In addition to forces, this technique readily permits the evaluation of out-of-equilibrium currents and the corresponding entropy production with a limited amount of data."]]></description>
<dc:subject>to:NB stochastic_differential_equations statistical_inference_for_stochastic_processes learning_theory time_series statistics to_read via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ed03f7fb2e45/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.03750">
    <title>[2005.03750] Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes</title>
    <dc:date>2020-05-29T13:38:49+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.03750</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network's universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation."]]></description>
<dc:subject>to:NB to_read prediction markov_models statistical_inference_for_stochastic_processes crutchfield.james_p. entropy_estimation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:01310a468c03/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<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:crutchfield.james_p."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://doi.org/10.1111/1368-423X.t01-1-00071">
    <title>Model selection tests for nonlinear dynamic models | The Econometrics Journal | Oxford Academic</title>
    <dc:date>2020-05-16T18:00:25+00:00</dc:date>
    <link>https://doi.org/10.1111/1368-423X.t01-1-00071</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper generalizes Vuong (1989) asymptotically normal tests for model selection in several important directions. First, it allows for incompletely parametrized models such as econometric models defined by moment conditions. Second, it allows for a broad class of estimation methods that includes most estimators currently used in practice. Third, it considers model selection criteria other than the models’ likelihoods such as the mean squared errors of prediction. Fourth, the proposed tests are applicable to possibly misspecified nonlinear dynamic models with weakly dependent heterogeneous data. Cases where the estimation methods optimize the model selection criteria are distinguished from cases where they do not. We also consider the estimation of the asymptotic variance of the difference between the competing models’ selection criteria, which is necessary to our tests. Finally, we discuss conditions under which our tests are valid. It is seen that the competing models must be essentially nonnested."]]></description>
<dc:subject>have_read to_reread model_selection hypothesis_testing statistics misspecification time_series statistical_inference_for_stochastic_processes vuong.quang to_teach:data_over_space_and_time re:HEAS in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:513c1caa4d37/</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:to_reread"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:misspecification"/>
	<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:vuong.quang"/>
	<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: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/0912.4480">
    <title>[0912.4480] Consistency of the maximum likelihood estimator for general hidden Markov models</title>
    <dc:date>2020-05-12T23:48:06+00:00</dc:date>
    <link>https://arxiv.org/abs/0912.4480</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is strongly consistent under a rather minimal set of assumptions. As special cases of our main result, we obtain consistency in a large class of nonlinear state space models, as well as general results on linear Gaussian state space models and finite state models. A novel aspect of our approach is an information-theoretic technique for proving identifiability, which does not require an explicit representation for the relative entropy rate. Our method of proof could therefore form a foundation for the investigation of MLE consistency in more general dependent and non-Markovian time series. Also of independent interest is a general concentration inequality for V-uniformly ergodic Markov chains."]]></description>
<dc:subject>to:NB have_read markov_models statistical_inference_for_stochastic_processes statistics_on_manifolds time_series</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:45a70689d38a/</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:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<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:statistics_on_manifolds"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1910.01004">
    <title>[1910.01004] Parameter estimation for SPDEs based on discrete observations in time and space</title>
    <dc:date>2020-01-12T23:02:20+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.01004</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in both coordinates, we prove central limit theorems for realized quadratic variations based on temporal and spatial increments as well as on double increments in time and space. Resulting method of moments estimators for the diffusivity and the volatility parameter inherit the asymptotic normality and can be constructed robustly with respect to the sampling frequencies in time and space. Upper and lower bounds reveal that in general the optimal convergence rate for joint estimation of the parameters is slower than the usual parametric rate. The theoretical results are illustrated in a numerical example."]]></description>
<dc:subject>to:NB statistical_inference_for_stochastic_processes stochastic_differential_equations spatio-temporal_statistics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d13b02320e01/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1807.05748">
    <title>[1807.05748] Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching</title>
    <dc:date>2019-11-10T21:46:11+00:00</dc:date>
    <link>https://arxiv.org/abs/1807.05748</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time increments and arbitrary sparseness, which is in contrast with gradient matching that does not optimize simulated responses. We formulate sensitivity equations for learning and demonstrate that our general stochastic distribution optimisation leads to robust and efficient learning of SDE systems."]]></description>
<dc:subject>to:NB stochastic_differential_equations statistical_inference_for_stochastic_processes gaussian_processes statistics nonparametrics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5db7dca15d4e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gaussian_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.05014">
    <title>[1809.05014] Statistical Estimation of Ergodic Markov Chain Kernel over Discrete State Space</title>
    <dc:date>2019-10-30T13:36:45+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.05014</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax sample complexity of estimation with respect to the operator infinity norm, while in the countably infinite case, we analyze the problem with respect to a natural entry-wise norm derived from total variation. We show that in both cases, the sample complexity is governed by the mixing properties of the unknown chain, for which, in the finite-state case, there are known finite-sample estimators with fully empirical confidence intervals."]]></description>
<dc:subject>to:NB markov_models statistical_inference_for_stochastic_processes statistics time_series kith_and_kin kontorovich.aryeh to_teach:data_over_space_and_time</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6bd3e4577c01/</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:statistical_inference_for_stochastic_processes"/>
	<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:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kontorovich.aryeh"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1910.04832">
    <title>[1910.04832] Learning interaction kernels in heterogeneous systems of agents from multiple trajectories</title>
    <dc:date>2019-10-24T14:08:30+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.04832</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct estimators that are guaranteed to converge in a suitable L2 space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm based on least squares, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and produce accurate predictions of dynamics in relative large time intervals, even when they are learned from data collected in short time intervals."]]></description>
<dc:subject>to:NB interacting_particle_systems statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ab103e2c9b23/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1910.04221">
    <title>[1910.04221] Likelihood-based Inference for Partially Observed Epidemics on Dynamic Networks</title>
    <dc:date>2019-10-11T16:36:27+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.04221</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic SIR model, in order to describe the interplay between epidemic dynamics on a network and network link changes. A Markov chain Monte Carlo framework is developed for likelihood-based inference from partial epidemic observations, with a novel data augmentation algorithm specifically designed to deal with missing individual recovery times under the dynamic network setting. Through a series of simulation experiments, we demonstrate the validity and flexibility of the model as well as the efficacy and efficiency of the data augmentation inference scheme. The model is also applied to a recent real-world dataset on influenza-like-illness transmission with high-resolution social contact tracking records."]]></description>
<dc:subject>epidemics_on_networks state-space_models statistical_inference_for_stochastic_processes statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e4dc67bf4832/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:epidemics_on_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.05517">
    <title>[1908.05517] Epidemic models on social networks -- with inference</title>
    <dc:date>2019-08-16T16:40:59+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.05517</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large population proporties of them are presented. Focus is then shifted to statistical methodology: what can be estimated and how, depending on the underlying network, transmission model and the available data? This survey paper discusses several different scenarios, also giving references to publications where more details can be found."]]></description>
<dc:subject>epidemics_on_networks statistical_inference_for_stochastic_processes in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1f661e2e8f7f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:epidemics_on_networks"/>
	<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:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1712.01572">
    <title>[1712.01572] Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces</title>
    <dc:date>2019-08-15T20:46:18+00:00</dc:date>
    <link>https://arxiv.org/abs/1712.01572</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the dynamics onto the dominant slow processes, or to separate superimposed signals. We extend transfer operator theory to reproducing kernel Hilbert spaces and show that these operators are related to Hilbert space representations of conditional distributions, known as conditional mean embeddings in the machine learning community. Moreover, numerical methods to compute empirical estimates of these embeddings are akin to data-driven methods for the approximation of transfer operators such as extended dynamic mode decomposition and its variants. One main benefit of the presented kernel-based approaches is that these methods can be applied to any domain where a similarity measure given by a kernel is available. We illustrate the results with the aid of guiding examples and highlight potential applications in molecular dynamics as well as video and text data analysis."]]></description>
<dc:subject>dynamical_systems statistical_inference_for_stochastic_processes in_NB kernel_methods hilbert_space koopman_operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:281f6ae34aef/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:koopman_operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.05172">
    <title>[1904.05172] Modeling a Hidden Dynamical System Using Energy Minimization and Kernel Density Estimates</title>
    <dc:date>2019-08-08T14:20:36+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.05172</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined by an underlying hidden dynamical system. Our work is inspired by earlier work on the use of KDE to detect shipping anomalies using high-density, high-quality automated information system (AIS) data as well as our own earlier work in trajectory modeling. We focus specifically on the sparse, noisy trajectory reconstruction problem in which the data are (i) sparsely sampled and (ii) subject to an imperfect observer that introduces noise. Under certain regularity assumptions, we show that the constructed estimator minimizes a specific energy function defined over the trajectory as the number of samples obtained grows."

Published version: https://doi.org/10.1103/PhysRevE.100.042137]]></description>
<dc:subject>to:NB dynamical_systems time_series inference_to_latent_objects statistics statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cc3ca7d4c683/</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:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inference_to_latent_objects"/>
	<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/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/1907.10679">
    <title>[1907.10679] Complete maximum likelihood estimation for SEIR epidemic models: theoretical development</title>
    <dc:date>2019-07-30T17:54:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1907.10679</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions between states of the population. The SEIR models consist of random dynamical equations for each state (S, E, I and R) involving driving events for the process. We characterize some special types of SEIR Markov chain models in the class including: (1) when birth and death are zero or non-zero, and (2) when the incubation and infectious periods are constant or random. A detailed parameter estimation applying the maximum likelihood estimation technique and expectation maximization algorithm are presented for this study. Numerical simulation results are given to validate the epidemic models."]]></description>
<dc:subject>to:NB epidemic_models time_series statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2d4ba83904b0/</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:epidemic_models"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.08720">
    <title>[1906.08720] Boosting for Dynamical Systems</title>
    <dc:date>2019-06-21T19:28:58+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.08720</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a framework of boosting for learning and control in environments that maintain a state. Leveraging methods for online learning with memory and for online boosting, we design an efficient online algorithm that can provably improve the accuracy of weak-learners in stateful environments. As a consequence, we give efficient boosting algorithms for both prediction and the control of dynamical systems. Empirical evaluation on simulated and real data for both control and prediction supports our theoretical findings."]]></description>
<dc:subject>to:NB ensemble_methods learning_theory dynamical_systems control_theory_and_control_engineering statistics time_series statistical_inference_for_stochastic_processes hazan.elad</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7e6510daea86/</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:ensemble_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<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: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:hazan.elad"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s11222-018-9827-1">
    <title>Importance sampling for partially observed temporal epidemic models | SpringerLink</title>
    <dc:date>2019-06-19T20:45:07+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s11222-018-9827-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present an importance sampling algorithm that can produce realisations of Markovian epidemic models that exactly match observations, taken to be the number of a single event type over a period of time. The importance sampling can be used to construct an efficient particle filter that targets the states of a system and hence estimate the likelihood to perform Bayesian inference. When used in a particle marginal Metropolis Hastings scheme, the importance sampling provides a large speed-up in terms of the effective sample size per unit of computational time, compared to simple bootstrap sampling. The algorithm is general, with minimal restrictions, and we show how it can be applied to any continuous-time Markov chain where we wish to exactly match the number of a single event type over a period of time."

]]></description>
<dc:subject>to:NB particle_filters epidemic_models stochastic_processes statistical_inference_for_stochastic_processes statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ad479c1c442d/</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:epidemic_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12360?af=R">
    <title>Inference for ergodic diffusions plus noise - Nakakita - 2019 - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2019-06-15T16:55:12+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12360?af=R</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We research an adaptive maximum‐likelihood–type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation noise, the diffusion parameter, and the drift one of the latent diffusion process. Moreover, it can lessen the computational burden compared to simultaneous maximum likelihood–type estimation. In addition to adaptive estimation, we propose a test to see if noise exists or not and analyze real data as the example such that the data contain observation noise with statistical significance."]]></description>
<dc:subject>to:NB stochastic_processes statistical_inference_for_stochastic_processes statistics time_series</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ba0d1c65f0ad/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.05566">
    <title>[1906.05566] Hypotheses testing and posterior concentration rates for semi-Markov processes</title>
    <dc:date>2019-06-14T12:45:44+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.05566</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and finite state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates."]]></description>
<dc:subject>to:NB stochastic_processes hypothesis_testing statistical_inference_for_stochastic_processes bayesian_consistency statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:44f148521a19/</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:hypothesis_testing"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.tandfonline.com/doi/full/10.1080/01621459.2019.1604367">
    <title>Panel Data Analysis via Mechanistic Models: Journal of the American Statistical Association: Vol 0, No 0</title>
    <dc:date>2019-06-14T12:41:16+00:00</dc:date>
    <link>https://www.tandfonline.com/doi/full/10.1080/01621459.2019.1604367</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared parameters while also having unit-specific parameters. To give the scientist flexibility in model specification, we are motivated to develop a framework for inference on panel data permitting the consideration of arbitrary nonlinear, partially observed panel models. We build on iterated filtering techniques that provide likelihood-based inference on nonlinear partially observed Markov process models for time series data. Our methodology depends on the latent Markov process only through simulation; this plug-and-play property ensures applicability to a large class of models. We demonstrate our methodology on a toy example and two epidemiological case studies. We address inferential and computational issues arising due to the combination of model complexity and dataset size."]]></description>
<dc:subject>to:NB statistics statistical_inference_for_stochastic_processes time_series ionides.edward to_read particle_filters</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f0c8d0b86853/</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: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:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ionides.edward"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1811.11834">
    <title>[1811.11834] Asymptotic Analysis of Model Selection Criteria for General Hidden Markov Models</title>
    <dc:date>2019-06-06T13:50:27+00:00</dc:date>
    <link>https://arxiv.org/abs/1811.11834</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper obtains analytical results for the asymptotic properties of Model Selection Criteria -- widely used in practice -- for a general family of hidden Markov models (HMMs), thereby substantially extending the related theory beyond typical i.i.d.-like model structures and filling in an important gap in the relevant literature. In particular, we look at the Bayesian and Akaike Information Criteria (BIC and AIC) and the model evidence. In the setting of nested classes of models, we prove that BIC and the evidence are strongly consistent for HMMs (under regularity conditions), whereas AIC is not weakly consistent. Numerical experiments support our theoretical results."]]></description>
<dc:subject>to:NB model_selection information_criteria state-space_models markov_models statistical_inference_for_stochastic_processes statistics singh.sumeetpal</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5adf62069468/</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:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_criteria"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:singh.sumeetpal"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.bj/1551862842">
    <title>Dahlhaus , Richter , Wu : Towards a general theory for nonlinear locally stationary processes</title>
    <dc:date>2019-05-25T03:02:16+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.bj/1551862842</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias expansions are proved for processes obeying an expansion in terms of the stationary approximation and derivative. In addition it is shown that this applies to some general nonlinear non-stationary Markov-models. In addition the results are applied to derive the asymptotic properties of maximum likelihood estimates of parameter curves in such models."]]></description>
<dc:subject>to:NB stochastic_processes non-stationarity statistical_inference_for_stochastic_processes wu.wei-biao</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e1403d6f4c18/</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:non-stationarity"/>
	<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:wu.wei-biao"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.bj/1544605253">
    <title>Lehéricy : Consistent order estimation for nonparametric hidden Markov models</title>
    <dc:date>2019-05-25T03:00:08+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.bj/1544605253</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of estimating the number of hidden states (the order) of a nonparametric hidden Markov model (HMM). We propose two different methods and prove their almost sure consistency without any prior assumption, be it on the order or on the emission distributions. This is the first time a consistency result is proved in such a general setting without using restrictive assumptions such as a priori upper bounds on the order or parametric restrictions on the emission distributions. Our main method relies on the minimization of a penalized least squares criterion. In addition to the consistency of the order estimation, we also prove that this method yields rate minimax adaptive estimators of the parameters of the HMM – up to a logarithmic factor. Our second method relies on estimating the rank of a matrix obtained from the distribution of two consecutive observations. Finally, numerical experiments are used to compare both methods and study their ability to select the right order in several situations."]]></description>
<dc:subject>to:NB model_selection markov_models state-space_models statistics statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:de655588d7d3/</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:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<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://projecteuclid.org/euclid.ss/1439220716">
    <title>Kantas , Doucet , Singh , Maciejowski , Chopin : On Particle Methods for Parameter Estimation in State-Space Models</title>
    <dc:date>2019-05-25T02:34:25+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.ss/1439220716</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, in most applications, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard particle methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive review of particle methods that have been proposed to perform static parameter estimation in state-space models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models."]]></description>
<dc:subject>to:NB particle_filters statistical_inference_for_stochastic_processes state-space_models statistics time_series to_teach:data_over_space_and_time have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:eb99758930ca/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<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:to_teach:data_over_space_and_time"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.ssu/1447165229">
    <title>McGoff , Mukherjee , Pillai : Statistical inference for dynamical systems: A review</title>
    <dc:date>2019-05-25T02:31:11+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.ssu/1447165229</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The topic of statistical inference for dynamical systems has been studied widely across several fields. In this survey we focus on methods related to parameter estimation for nonlinear dynamical systems. Our objective is to place results across distinct disciplines in a common setting and highlight opportunities for further research."]]></description>
<dc:subject>dynamical_systems statistical_inference_for_stochastic_processes stochastic_processes statistics re:almost_none re:stacs have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:98dfc7d60875/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:stacs"/>
	<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="https://www.cambridge.org/9781316649466">
    <title>Applied stochastic differential equations</title>
    <dc:date>2019-05-14T15:49:04+00:00</dc:date>
    <link>https://www.cambridge.org/9781316649466</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods."

--- PDF from the authors somewhere.]]></description>
<dc:subject>to:NB books:noted stochastic_differential_equations stochastic_processes filtering time_series statistical_inference_for_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:be7b53a609b6/</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_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<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:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1903.01608">
    <title>[1903.01608] Theoretical guarantees for sampling and inference in generative models with latent diffusions</title>
    <dc:date>2019-05-13T13:37:45+00:00</dc:date>
    <link>https://arxiv.org/abs/1903.01608</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion. We make the following contributions: 
"We provide a unified viewpoint on both sampling and variational inference in such generative models through the lens of stochastic control. 
"We quantify the expressiveness of diffusion-based generative models. Specifically, we show that one can efficiently sample from a wide class of terminal target distributions by choosing the drift of the latent diffusion from the class of multilayer feedforward neural nets, with the accuracy of sampling measured by the Kullback-Leibler divergence to the target distribution. 
"Finally, we present and analyze a scheme for unbiased simulation of generative models with latent diffusions and provide bounds on the variance of the resulting estimators. This scheme can be implemented as a deep generative model with a random number of layers."

Slides: https://uofi.app.box.com/s/k8et7xq1b43w3dh7ho5qesot7hk46irj]]></description>
<dc:subject>to:NB stochastic_processes inference_to_latent_objects statistical_inference_for_stochastic_processes neural_networks variational_inference raginsky.maxim have_skimmed re:almost_none control_theory_and_control_engineering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7cb225a6e2fa/</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:inference_to_latent_objects"/>
	<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:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variational_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/book/10.1002/9781118632321">
    <title>Extremes and Recurrence in Dynamical Systems | Wiley Online Books</title>
    <dc:date>2019-01-07T17:18:43+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/book/10.1002/9781118632321</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features:
"• A careful examination of how a dynamical system can serve as a generator of stochastic processes
"• Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes
"• Several examples of analysis of extremes in a physical and geophysical context
"• A final summary of the main results presented along with a guide to future research projects
"• An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts
"Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science."]]></description>
<dc:subject>to:NB books:noted extreme_values dynamical_systems time_series statistical_inference_for_stochastic_processes statistics downloaded recurrence_times</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cff72412f8a2/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:extreme_values"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:recurrence_times"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>