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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://link.springer.com/chapter/10.1007/978-3-662-03738-6_7"/>
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	<rdf:li rdf:resource="http://proceedings.mlr.press/v139/kandiros21a.html"/>
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  </channel><item rdf:about="https://arxiv.org/abs/2512.15605">
    <title>[2512.15605] Autoregressive Language Models are Secretly Energy-Based Models: Insights into the Lookahead Capabilities of Next-Token Prediction</title>
    <dc:date>2026-01-27T03:26:30+00:00</dc:date>
    <link>https://arxiv.org/abs/2512.15605</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet naturally characterize the optimal policy in post-training alignment. In this paper, we provide a unified view of these two model classes. Taking the chain rule of probability as a starting point, we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning. Building upon this bijection, we derive the equivalence between supervised learning of ARMs and EBMs. Furthermore, we analyze the distillation of EBMs into ARMs by providing theoretical error bounds. Our results provide insights into the ability of ARMs to plan ahead, despite being based on the next-token prediction paradigm."


--- ETA after skimming: Pretty sure this is just the usual Gibbs-Markov equivalence, but check carefully later.]]></description>
<dc:subject>to:NB large_language_models_(so_called) gibbs_distributions random_fields markov_models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:00b414131396/</dc:identifier>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03552-4">
    <title>Gaussian concentration bounds for probabilistic cellular automata | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:23:09+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03552-4</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish the conservation of GCB and, in the high-noise regime, demonstrate that GCB holds for the unique stationary measure. Additionally, we prove the equivalence of GCB for the space-time measure and its spatial marginals in the case of contractive probabilistic cellular automata. Furthermore, we explore the relationship between (non)-uniqueness and GCB in the context of space-time Gibbs measures for PCA and illustrate these results with examples."]]></description>
<dc:subject>to:NB concentration_of_measure random_fields stochastic_processes cellular_automata chazottes.jean-rene</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9f0c1770e032/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cellular_automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chazottes.jean-rene"/>
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<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-30/issue-1/The-screening-effect-in-Kriging/10.1214/aos/1015362194.full">
    <title>The screening effect in Kriging</title>
    <dc:date>2023-10-05T01:22:50+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-30/issue-1/The-screening-effect-in-Kriging/10.1214/aos/1015362194.full</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When predicting the value of a stationary random field at a location x in some region in which one has a large number of observations, it may be difficult to compute the optimal predictor. One simple way to reduce the computational burden is to base the predictor only on those observations nearest to x. As long as the number of observations used in the predictor is sufficiently large, one might generally expect the best predictor based on these observations to be nearly optimal relative to the best predictor using all observations. Indeed, this phenomenon has been empirically observed in numerous circumstances and is known as the screening effect in the geostatistical literature. For linear predictors, when observations are on a regular grid, this work proves that there generally is a screening effect as the grid becomes increasingly dense. This result requires that, at high frequencies, the spectral density of the random field not decay faster than algebraically and not vary too quickly. Examples demonstrate that there may be no screening effect if these conditions on the spectral density are violated."]]></description>
<dc:subject>have_skimmed spatial_statistics random_fields statistics to_teach:data_over_space_and_time in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:eb89cb46ceea/</dc:identifier>
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	<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"/>
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<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-18/issue-2/Uniform-Asymptotic-Optimality-of-Linear-Predictions-of-a-Random-Field/10.1214/aos/1176347629.full">
    <title>Uniform Asymptotic Optimality of Linear Predictions of a Random Field Using an Incorrect Second-Order Structure</title>
    <dc:date>2023-10-04T20:23:28+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-18/issue-2/Uniform-Asymptotic-Optimality-of-Linear-Predictions-of-a-Random-Field/10.1214/aos/1176347629.full</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>spatial_statistics random_fields have_skimmed to_teach:data_over_space_and_time in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9a75106c9994/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data_over_space_and_time"/>
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</item>
<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-16/issue-1/Asymptotically-Efficient-Prediction-of-a-Random-Field-with-a-Misspecified/10.1214/aos/1176350690.full">
    <title>Asymptotically Efficient Prediction of a Random Field with a Misspecified Covariance Function</title>
    <dc:date>2023-10-04T20:22:51+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-16/issue-1/Asymptotically-Efficient-Prediction-of-a-Random-Field-with-a-Misspecified/10.1214/aos/1176350690.full</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[--- Reveals to me that I have no intuition for when two Gaussian random fields are mutually absolutely continuous in the in-fill limit.  (Two stationary and ergodic time-series are MAC in the time-going-to-infinity limit iff they are identical.  [Otherwise, by ergodicity, each of them puts probability 1 on an event to which the other assigns probability 0.]  But that doesn't apply here!)]]></description>
<dc:subject>spatial_statistics have_skimmed to_teach:data_over_space_and_time random_fields in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:877383588193/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
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</item>
<item rdf:about="https://link.springer.com/chapter/10.1007/978-3-662-03738-6_7">
    <title>Communication Norms and the Collective Cognitive Performance of “Invisible Colleges” | SpringerLink</title>
    <dc:date>2023-05-10T02:44:02+00:00</dc:date>
    <link>https://link.springer.com/chapter/10.1007/978-3-662-03738-6_7</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Scientific research communities may be studied as social networks within which ideas or statements circulate, acquire validity as reliable knowledge, and are recombined to generate further new ideas. Social networks also form the locus for the transmission of tacit knowledge and skills requisite to the interpretation and operationalization of scientific statements. These extensive, yet informal structures of inter-personal knowledge-transactions have been referred to as constituting “invisible colleges”. This paper develops an abstract and highly stylized account of the communications structure of an invisible college, and examines its collective epistemological performance by employing concepts and results from Markov random field theory."

--- Now does this version (from 1996?) differ from the reprint I still have from the 1998 SFI conference?]]></description>
<dc:subject>in_NB collective_cognition sociology_of_science david.paul_a. science_as_a_social_process random_fields voter_model heard_the_talk cleaning_out_the_filing_cabinet_for_the_first_time_since_2005</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f2dd9bd2f1fb/</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:collective_cognition"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sociology_of_science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:david.paul_a."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:science_as_a_social_process"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:voter_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2305.00322">
    <title>[2305.00322] Toward $L_infty$-recovery of Nonlinear Functions: A Polynomial Sample Complexity Bound for Gaussian Random Fields</title>
    <dc:date>2023-05-05T01:47:16+00:00</dc:date>
    <link>https://arxiv.org/abs/2305.00322</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many machine learning applications require learning a function with a small worst-case error over the entire input domain, that is, the L∞-error, whereas most existing theoretical works only guarantee recovery in average errors such as the L2-error. L∞-recovery from polynomial samples is even impossible for seemingly simple function classes such as constant-norm infinite-width two-layer neural nets. This paper makes some initial steps beyond the impossibility results by leveraging the randomness in the ground-truth functions. We prove a polynomial sample complexity bound for random ground-truth functions drawn from Gaussian random fields. Our key technical novelty is to prove that the degree-k spherical harmonics components of a function from Gaussian random field cannot be spiky in that their L∞/L2 ratios are upperbounded by O(dlnk‾‾‾‾√) with high probability. In contrast, the worst-case L∞/L2 ratio for degree-k spherical harmonics is on the order of Ω(min{dk/2,kd/2})."

--- This sounds interesting, but it also seems to say that Gaussian random fields generate especially smooth functions (with high probability), casting doubt on their suitability as a general prior.  (Of course I think there's no such thing as a general
prior.)]]></description>
<dc:subject>approximation learning_theory random_fields in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fb73aea45ac1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2112.01288">
    <title>[2112.01288] How to quantify fields or textures? A guide to the scattering transform</title>
    <dc:date>2023-03-21T15:02:11+00:00</dc:date>
    <link>https://arxiv.org/abs/2112.01288</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power spectrum analysis, which is often too limited, or the use of convolutional neural networks (CNNs), which require large training sets and lack interpretability. In this paper, we advocate for the use of the scattering transform (Mallat 2012), a powerful statistic which borrows mathematical ideas from CNNs but does not require any training, and is interpretable. We show that it provides a relatively compact set of summary statistics with visual interpretation and which carries most of the relevant information in a wide range of scientific applications. We present a non-technical introduction to this estimator and we argue that it can benefit data analysis, comparison to models and parameter inference in many fields of science. Interestingly, understanding the core operations of the scattering transform allows one to decipher many key aspects of the inner workings of CNNs."]]></description>
<dc:subject>pattern_recognition spatial_statistics random_fields neural_networks via:mraginsky in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4b7134f912fc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:pattern_recognition"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</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://arxiv.org/abs/2206.03769">
    <title>[2206.03769] Renormalization group and generalized Central Limit Theorems: The critical probability distributions of the order parameter of the Ising model</title>
    <dc:date>2022-06-09T08:20:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.03769</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We show that the functional renormalization group (FRG) allows for the generalization of the central limit theorem to strongly correlated random variables. On the example of the three-dimensional Ising model at criticality and using the simplest implementation of the FRG, we compute the probability distribution functions of the order parameter or equivalently its logarithm, called the rate functions in large deviations theory. We compute the entire family of universal scaling functions, obtained in the limit where the system size L and the correlation length of the infinite system ξ∞ diverge, with the ratio ζ=L/ξ∞ held fixed. It compares very accurately with numerical simulations."]]></description>
<dc:subject>to:NB stochastic_processes random_fields central_limit_theorem ising_model renormalization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0ddadeac6846/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ising_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:renormalization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.02365">
    <title>[2102.02365] Wind Field Reconstruction with Adaptive Random Fourier Features</title>
    <dc:date>2022-04-22T12:29:46+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.02365</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared to a set of benchmark methods including Kriging and Inverse distance weighting. Random Fourier features is a linear model β(xx)=∑Kk=1βkeiωkxx approximating the velocity field, with frequencies ωk randomly sampled and amplitudes βk trained to minimize a loss function. We include a physically motivated divergence penalty term |∇⋅β(xx)|2, as well as a penalty on the Sobolev norm. We derive a bound on the generalization error and derive a sampling density that minimizes the bound. Following (arXiv:2007.10683 [math.NA]), we devise an adaptive Metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models."]]></description>
<dc:subject>to:NB to_read spatial_statistics smoothing random_fields random_features to_teach:data_over_space_and_time via:?</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:28210c4cccd9/</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:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_features"/>
	<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:via:?"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://proceedings.mlr.press/v139/kandiros21a.html">
    <title>Statistical Estimation from Dependent Data</title>
    <dc:date>2021-07-11T16:44:59+00:00</dc:date>
    <link>http://proceedings.mlr.press/v139/kandiros21a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioning on their feature vectors, but dependent, capturing settings where e.g. these observations are collected on a spatial domain, a temporal domain, or a social network, which induce dependencies. We model these dependencies in the language of Markov Random Fields and, importantly, allow these dependencies to be substantial, i.e. do not assume that the Markov Random Field capturing these dependencies is in high temperature. As our main contribution we provide algorithms and statistically efficient estimation rates for this model, giving several instantiations of our bounds in logistic regression, sparse logistic regression, and neural network regression settings with dependent data. Our estimation guarantees follow from novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a single sample."]]></description>
<dc:subject>to:NB learning_theory random_fields classifiers dependent_learning of_course_its_really_a_spin_glass statistics learning_under_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a1d41909f983/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:classifiers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dependent_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:of_course_its_really_a_spin_glass"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.03162">
    <title>[2107.03162] Distance covariance for random fields</title>
    <dc:date>2021-07-08T16:30:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.03162</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study an independence test based on distance correlation for random fields (X,Y). We consider the situations when (X,Y) is observed on a lattice with equidistant grid sizes and when (X,Y) is observed at random locations. We provide \asy\ theory for the sample distance correlation in both situations and show bootstrap consistency. The latter fact allows one to build a test for independence of X and Y based on the considered discretizations of these fields. We illustrate the performance of the bootstrap test in a simulation study involving fractional Brownian and infinite variance stable fields. The independence test is applied to Japanese meteorological data, which are observed over the entire area of Japan."]]></description>
<dc:subject>to:NB random_fields dependence_measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9ebc13e22e92/</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:dependence_measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.14145">
    <title>[2106.14145] An Approach to Causal Inference over Stochastic Networks</title>
    <dc:date>2021-06-30T02:51:15+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.14145</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Claiming causal inferences in network settings necessitates careful consideration of the often complex dependency between outcomes for actors. Of particular importance are treatment spillover or outcome interference effects. We consider causal inference when the actors are connected via an underlying network structure. Our key contribution is a model for causality when the underlying network is unobserved and the actor covariates evolve stochastically over time. We develop a joint model for the relational and covariate generating process that avoids restrictive separability assumptions and deterministic network assumptions that do not hold in the majority of social network settings of interest. Our framework utilizes the highly general class of Exponential-family Random Network models (ERNM) of which Markov Random Fields (MRF) and Exponential-family Random Graph models (ERGM) are special cases. We present potential outcome based inference within a Bayesian framework, and propose a simple modification to the exchange algorithm to allow for sampling from ERNM posteriors. We present results of a simulation study demonstrating the validity of the approach. Finally, we demonstrate the value of the framework in a case-study of smoking over time in the context of adolescent friendship networks."]]></description>
<dc:subject>to:NB network_data_analysis exponential_family_random_graphs random_fields handcock.mark causal_inference re:homophily_and_confounding statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1bf3c5d4ff92/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_family_random_graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:handcock.mark"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:homophily_and_confounding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.14458">
    <title>[2005.14458] Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression</title>
    <dc:date>2021-06-01T17:33:18+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.14458</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Random Forests (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data, which can also be used for targets other than the original mean estimation. We propose a novel forest construction for multivariate responses based on their joint conditional distribution, independent of the estimation target and the data model. It uses a new splitting criterion based on the MMD distributional metric, which is suitable for detecting heterogeneity in multivariate distributions. The induced weights define an estimate of the full conditional distribution, which in turn can be used for arbitrary and potentially complicated targets of interest. The method is very versatile and convenient to use, as we illustrate on a wide range of examples. The code is available as Python and R packages drf."]]></description>
<dc:subject>to:NB density_estimation random_fields buhlmann.peter ensemble_methods statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:35774f99f672/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:buhlmann.peter"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ensemble_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1911.06770">
    <title>[1911.06770] Probabilistic Foundations of Spatial Mean-field Models in Ecology and Applications</title>
    <dc:date>2021-05-30T20:44:54+00:00</dc:date>
    <link>https://arxiv.org/abs/1911.06770</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field limit for a general class of stochastic models representing each individual ecological event in the limit of large system size. The proof relies on classical stochastic coupling techniques that we generalize to cover spatially extended interactions. The mean-field limit is a spatially extended non-Markovian process characterized by nonlocal integro-differential equations describing the evolution of the probability for a patch of land to be in a given state (the generalized Kolmogorov equations of the process, GKEs). We thus provide an accessible general framework for spatially extending many classical finite-state models from ecology and population dynamics. We demonstrate the practical effectiveness of our approach through a detailed comparison of our limiting spatial model and the finite-size version of a specific savanna-forest model, the so-called Staver-Levin model. There is remarkable dynamic consistency between the GKEs and the finite-size system, in spite of almost sure forest extinction in the finite-size system. To resolve this apparent paradox, we show that the extinction rate drops sharply when nontrivial equilibria emerge in the GKEs, and that the finite-size system's quasi-stationary distribution (stationary distribution conditional on non-extinction) closely matches the bifurcation diagram of the GKEs. Furthermore, the limit process can support periodic oscillations of the probability distribution, thus providing an elementary example of a jump process that does not converge to a stationary distribution. In spatially extended settings, environmental heterogeneity can lead to waves of invasion and front-pinning phenomena."]]></description>
<dc:subject>to:NB ecology macro_from_micro random_fields levin.simon</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e6ad02fba8ee/</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:ecology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macro_from_micro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:levin.simon"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.09549">
    <title>[2012.09549] Stochastic Lotka-Volterra Competitive Reaction-Diffusion Systems Perturbed by Space-Time White Noise: Modeling and Analysis</title>
    <dc:date>2021-05-13T05:24:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.09549</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation enables spatial dependence of the species. In addition, the noise process is allowed to be space-time white noise. In this work, wellposedness, regularity of solutions, existence of density, and existence of an invariant measure for stochastic reaction-diffusion systems with non-Lipschitz and non-linear growth coefficients and multiplicative noise are considered. By combining the random field approach and infinite integration theory approach in SPDEs for mild solutions, analysis is carried out. Then this paper develops a Lotka-Volterra competitive system under general setting; longtime properties are studied with the help of newly developed tools in stochastic calculus."]]></description>
<dc:subject>to:NB random_fields ecology stochastic_differential_equations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:022cb07d27b9/</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:ecology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2007.10874">
    <title>[2007.10874] Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields</title>
    <dc:date>2021-04-08T14:25:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.10874</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We obtain central limit theorems for stationary random fields employing a novel measure of dependence called θ-lex weak dependence. We show that this dependence notion is more general than strong mixing, i.e., it applies to a broader class of models. Moreover, we discuss hereditary properties for θ-lex and η-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general results apply to mixed moving average fields (MMAF in short) and ambit fields. We show general conditions such that MMAF and ambit fields, with the volatility field being an MMAF or a p-dependent random field, are weakly dependent. For all the models mentioned above, we give a complete characterization of their weak dependence coefficients and sufficient conditions to obtain the asymptotic normality of their sample moments. Finally, we give explicit computations of the weak dependence coefficients of MSTOU processes and analyze under which conditions the developed asymptotic theory applies to CARMA fields."]]></description>
<dc:subject>to:NB mixing dependence_measures random_fields central_limit_theorem stochastic_processes to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f6d72975cae5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dependence_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.11060">
    <title>[1904.11060] Normal Approximation in Large Network Models</title>
    <dc:date>2021-03-03T04:28:29+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.11060</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop a methodology for proving central limit theorems in network models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network size tends to infinity. In the presence of strategic interactions, network moments are generally complex functions of components, where a node's component consists of all alters to which it is directly or indirectly connected. We find that a modification of "exponential stabilization" conditions from the stochastic geometry literature provides a useful formulation of weak dependence for moments of this type. We establish a CLT for a network moments satisfying stabilization and provide a methodology for deriving primitive sufficient conditions for stabilization using results in branching process theory. We apply the methodology to static and dynamic models of network formation."]]></description>
<dc:subject>to:NB network_data_analysis statistics random_fields central_limit_theorem</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4680019e3ec7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.03801">
    <title>[2101.03801] Hidden Markov chains and fields with observations in Riemannian manifolds</title>
    <dc:date>2021-01-12T22:39:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.03801</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Hidden Markov chain, or Markov field, models, with observations in a Euclidean space, play a major role across signal and image processing. The present work provides a statistical framework which can be used to extend these models, along with related, popular algorithms (such as the Baum-Welch algorithm), to the case where the observations lie in a Riemannian manifold. It is motivated by the potential use of hidden Markov chains and fields, with observations in Riemannian manifolds, as models for complex signals and images."]]></description>
<dc:subject>to:NB markov_models state-space_models random_fields statistics_on_manifolds</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b0b4911debdd/</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:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.ss/1608541222">
    <title>Katzfuss , Guinness : A General Framework for Vecchia Approximations of Gaussian Processes</title>
    <dc:date>2020-12-21T14:09:14+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.ss/1608541222</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise term, we propose a generalization of the Vecchia (J. Roy. Statist. Soc. Ser. B 50 (1988) 297–312) approach as a framework for GP approximations. We show that our general Vecchia approach contains many popular existing GP approximations as special cases, allowing for comparisons among the different methods within a unified framework. Representing the models by directed acyclic graphs, we determine the sparsity of the matrices necessary for inference, which leads to new insights regarding the computational properties. Based on these results, we propose a novel sparse general Vecchia approximation, which ensures computational feasibility for large spatial datasets but can lead to considerable improvements in approximation accuracy over Vecchia’s original approach. We provide several theoretical results and conduct numerical comparisons. We conclude with guidelines for the use of Vecchia approximations in spatial statistics."]]></description>
<dc:subject>to:NB approximation computational_statistics random_fields gaussian_processes stochastic_processes statistics_on_manifolds</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:21d74c2d020c/</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:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gaussian_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.06371">
    <title>[2005.06371] Nonparametric regression for locally stationary random fields under stochastic sampling design</title>
    <dc:date>2020-12-16T17:47:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.06371</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) {Xs,An:s∈Rn} in ℝp observed at irregularly spaced locations in Rn=[0,An]d⊂ℝd. We first derive the uniform convergence rate of general kernel estimators, followed by the asymptotic normality of an estimator for the mean function of the model. Moreover, we consider additive models to avoid the curse of dimensionality arising from the dependence of the convergence rate of estimators on the number of covariates. Subsequently, we derive the uniform convergence rate and joint asymptotic normality of the estimators for additive functions. We also introduce approximately mn-dependent RFs to provide examples of LSRFs. We find that these RFs include a wide class of Lévy-driven moving average RFs."]]></description>
<dc:subject>to:NB random_fields spatial_statistics spatio-temporal_statistics smoothing nonparametrics regression additive_models statistics to_teach:data_over_space_and_time kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9759167da0d4/</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:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:additive_models"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</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://arxiv.org/abs/2012.05784">
    <title>[2012.05784] Detecting Structured Signals in Ising Models</title>
    <dc:date>2020-12-12T19:58:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.05784</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models (Erdős-Rényi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising Models, and demonstrate the beneficial behavior of criticality in the detection of strictly lower signals. As a by-product of our proof technique, we develop sharp control on mixing and spin-spin correlation for several Mean-Field type Ising Models in all regimes of temperature -- which might be of independent interest."]]></description>
<dc:subject>to:NB ising_model hypothesis_testing random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:aca767ba90f5/</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:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/full/10.1002/env.1102?casa_token=ocbU79FU42EAAAAA%3AQDyFS0-w-z1X4iyTEguPeij1WKqyFlab8iL4qHNhaVg8STIrrUbdwgliDave2STG6TP7Ue6-ZfbM6g">
    <title>Autologistic models for binary data on a lattice - Hughes - 2011 - Environmetrics - Wiley Online Library</title>
    <dc:date>2020-11-21T03:45:52+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/full/10.1002/env.1102?casa_token=ocbU79FU42EAAAAA%3AQDyFS0-w-z1X4iyTEguPeij1WKqyFlab8iL4qHNhaVg8STIrrUbdwgliDave2STG6TP7Ue6-ZfbM6g</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The autologistic model is a Markov random field model for spatial binary data. Because it can account for both statistical dependence among the data and for the effects of potential covariates, the autologistic model is particularly suitable for problems in many fields, including ecology, where binary responses, indicating the presence or absence of a certain plant or animal species, are observed over a two‐dimensional lattice. We consider inference and computation for two models: the original autologistic model due to Besag, and the centered autologistic model proposed recently by Caragea and Kaiser. Parameter estimation and inference for these models is a notoriously difficult problem due to the complex form of the likelihood function. We study pseudolikelihood (PL), maximum likelihood (ML), and Bayesian approaches to inference and describe ways to optimize the efficiency of these algorithms and the perfect sampling algorithms upon which they depend, taking advantage of parallel computing when possible. We conduct a simulation study to investigate the effects of spatial dependence and lattice size on parameter inference, and find that inference for regression parameters in the centered model is reliable only for reasonably large lattices (n > 900) and no more than moderate spatial dependence. When the lattice is large enough, and the dependence small enough, to permit reliable inference, the three approaches perform comparably, and so we recommend the PL approach for its easier implementation and much faster execution."]]></description>
<dc:subject>to:NB random_fields ecology spatial_statistics birds markov_models ising_model logistic_regression to_teach:data_over_space_and_time of_course_its_really_a_spin_glass have_skimmed</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f06130584e87/</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:ecology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:birds"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ising_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:logistic_regression"/>
	<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:of_course_its_really_a_spin_glass"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1198/108571105X46543">
    <title>Modeling spatial-temporal binary data using Markov random fields | SpringerLink</title>
    <dc:date>2020-11-21T03:42:14+00:00</dc:date>
    <link>https://link.springer.com/article/10.1198/108571105X46543</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["An autologistic regression model consists of a logistic regression of a response variable on explanatory variables and an autoregression on responses at neighboring locations on a lattice. It is a Markov random field with pairwise spatial dependence and is a popular tool for modeling spatial binary responses. In this article, we add a temporal component to the autologistic regression model for spatial-temporal binary data. The spatial-temporal autologistic regression model captures the relationship between a binary response and potential explanatory variables, and adjusts for both spatial dependence and temporal dependence simultaneously by a space-time Markov random field. We estimate the model parameters by maximum pseudo-likelihood and obtain optimal prediction of future responses on the lattice by a Gibbs sampler. For illustration, the method is applied to study the outbreaks of southern pine bettle in North Carolina. We also discuss the generality of our approach for modeling other types of spatial-temporal lattice data."]]></description>
<dc:subject>to:NB spatio-temporal_statistics random_fields markov_models insects have_skimmed to_teach:data_over_space_and_time of_course_its_really_a_spin_glass ising_model logistic_regression</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:01152ca5b0a6/</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:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:insects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<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:of_course_its_really_a_spin_glass"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ising_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:logistic_regression"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1023/A:1018553807765">
    <title>Modelling the distribution of plant species using the autologistic regression model | SpringerLink</title>
    <dc:date>2020-11-21T03:41:58+00:00</dc:date>
    <link>https://link.springer.com/article/10.1023/A:1018553807765</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida."]]></description>
<dc:subject>to:NB ecology spatial_statistics markov_models random_fields have_skimmed to_teach:data_over_space_and_time of_course_its_really_a_spin_glass ising_model logistic_regression</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1e0bc6629a0a/</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:ecology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<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:of_course_its_really_a_spin_glass"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ising_model"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:logistic_regression"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.09690">
    <title>[2011.09690] Onsager-Machlup action functional for stochastic partial differential equations with Levy noise</title>
    <dc:date>2020-11-20T04:02:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.09690</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian motion. This is achieved by applying the Girsanov transformation for probability measures and then by a path representation. This enables the investigation of the most probable transition path for infinite dimensional stochastic dynamical systems modeled by stochastic partial differential equations, by minimizing the Onsager-Machlup action functional."]]></description>
<dc:subject>to:NB stochastic_differential_equations stochastic_processes large_deviations to_read random_fields spatio-temporal_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c6c4c2511f68/</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:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://ieeexplore.ieee.org/document/8782628">
    <title>Testing Ising Models - IEEE Journals &amp; Magazine</title>
    <dc:date>2020-11-16T17:00:33+00:00</dc:date>
    <link>https://ieeexplore.ieee.org/document/8782628</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Given samples from an unknown multivariate distribution p, is it possible to distinguish whether p is the product of its marginals versus p being far from every product distribution? Similarly, is it possible to distinguish whether p equals a given distribution q versus p and q being far from each other? These problems of testing independence and goodnessof-fit have received enormous attention in statistics, information theory, and theoretical computer science, with sample-optimal algorithms known in several interesting regimes of parameters. Unfortunately, it has also been understood that these problems become intractable in large dimensions, necessitating exponential sample complexity. Motivated by the exponential lower bounds for general distributions as well as the ubiquity of Markov random fields (MRFs) in the modeling of high-dimensional distributions, we initiate the study of distribution testing on structured multivariate distributions, and in particular, the prototypical example of MRFs: the Ising Model. We demonstrate that, in this structured setting, we can avoid the curse of dimensionality, obtaining sample, and time efficient testers for independence and goodness-of-fit. One of the key technical challenges we face along the way is bounding the variance of functions of the Ising model."]]></description>
<dc:subject>to:NB random_fields hypothesis_testing statistics ising_model</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f131bb3148ca/</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:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ising_model"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12556">
    <title>A local limit theorem for linear random fields - Fortune - - Journal of Time Series Analysis - Wiley Online Library</title>
    <dc:date>2020-09-28T19:27:43+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/jtsa.12556</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this article, we establish a local limit theorem for linear fields of random variables constructed from i.i.d. innovations each with finite second moment. When the coefficients are absolutely summable we do not restrict the region of summation. However, when the coefficients are only square‐summable we add the variables on unions of rectangle and we impose regularity conditions on the coefficients depending on the number of rectangles considered. Our results are new also for the dimension 1, that is, for linear sequences of random variables. The examples include the fractionally integrated processes for which the results of a simulation study is also included."]]></description>
<dc:subject>to:NB stochastic_processes random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:562fed0a71f2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1911.12198">
    <title>[1911.12198] Strong structure recovery for partially observed discrete Markov random fields on graphs</title>
    <dc:date>2020-01-30T23:52:29+00:00</dc:date>
    <link>https://arxiv.org/abs/1911.12198</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a penalized maximum likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field, that can be partially observed. We prove the almost sure convergence of the estimator in the case of a finite or countable infinite set of variables. In the finite case, the underlying graph can be recovered with probability one, while in the countable infinite case we can recover any finite subgraph with probability one, by allowing the candidate neighborhoods to grow with the sample size n. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed."]]></description>
<dc:subject>to:NB random_fields markov_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:80cc0dfb4787/</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:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.ejs/1573009454">
    <title>Chen , Wang : Distributional properties and estimation in spatial image clustering</title>
    <dc:date>2019-11-25T15:56:21+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.ejs/1573009454</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Clusters of different objects are of great interest in many fields, such as agriculture and ecology. One kind of clustering methods is very different from the traditional statistical clustering analysis, which is based on discrete data points. This method of clustering defines clusters as the connected areas where a well-defined spatial random field is above certain threshold. The statistical properties, especially the distributional properties, of the defined clusters are vital for the studies of related fields. However, the available statistical techniques for analyzing clustering models are not applicable to these problems. We study the distribution properties of the clusters by defining a distribution function of the clusters rigorously and providing methods to estimate the spatial distribution function. Our results are illustrated by numerical experiments and an application to a real world problem.]]></description>
<dc:subject>spatial_statistics random_fields to_teach:data_over_space_and_time statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f86f8219aad8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<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:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1910.09645">
    <title>[1910.09645] Markov Random Fields for Collaborative Filtering</title>
    <dc:date>2019-10-24T13:44:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.09645</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we model the dependencies among the items that are recommended to a user in a collaborative-filtering problem via a Gaussian Markov Random Field (MRF). We build upon Besag's auto-normal parameterization and pseudo-likelihood, which not only enables computationally efficient learning, but also connects the areas of MRFs and sparse inverse covariance estimation with autoencoders and neighborhood models, two successful approaches in collaborative filtering. We propose a novel approximation for learning sparse MRFs, where the trade-off between recommendation-accuracy and training-time can be controlled. At only a small fraction of the training-time compared to various baselines, including deep nonlinear models, the proposed approach achieved competitive ranking-accuracy on all three well-known data-sets used in our experiments, and notably a 20% gain in accuracy on the data-set with the largest number of items."]]></description>
<dc:subject>to:NB random_fields collaborative_filtering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6716a868dae4/</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:collaborative_filtering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.10943">
    <title>[1909.10943] Bounded law of the iterated logarithms for stationary random fields</title>
    <dc:date>2019-09-26T03:47:31+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.10943</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields when the summation is done on rectangle. The study is done by the control of an appropriated maximal function. The case of functional of i.i.d. random fields, martingales with respect to the lexicographic order and orthomartingale is treated. Then results on projective conditions are derived. Applications to linear and Volterra random fields are given."]]></description>
<dc:subject>to:NB probability stochastic_processes random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:851c02d769e3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.06401">
    <title>[1909.06401] Fluctuations for Spatially Extended Hawkes Processes</title>
    <dc:date>2019-09-18T12:56:35+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.06401</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In a previous paper, it has been shown that the mean-field limit of spatially extended Hawkes processes is characterized as the unique solution u(t,x) of a neural field equation (NFE). The value u(t,x) represents the membrane potential at time t of a typical neuron located in position x, embedded in an infinite network of neurons. In the present paper, we complement this result by studying the fluctuations of such a stochastic system around its mean field limit u(t,x). Our first main result is a central limit theorem stating that the spatial distribution associated to these fluctuations converges to the unique solution of some stochastic differential equation driven by a Gaussian noise. In our second main result we show that the solutions of this stochastic differential equation can be well approximated by a stochastic version of the neural field equation satisfied by u(t,x). To the best of our knowledge, this result appears to be new in the literature."]]></description>
<dc:subject>to:NB point_processes stochastic_processes random_fields central_limit_theorem</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fd12d1a0a806/</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:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.08686">
    <title>[1809.08686] On the quenched CLT for stationary random fields under projective criteria</title>
    <dc:date>2019-09-15T14:46:54+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.08686</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Volný (2018) showed that the quenched CLT (central limit theorem) holds for ortho-martingale random fields. In this paper, we study the quenched CLT for a class of random fields larger than the ortho-martingales. To get the results, we impose sufficient conditions in terms of projective criteria under which the partial sums of a stationary random field admit an ortho-martingale approximation. More precisely, the sufficient conditions are of the Hannan's projective type. As applications, we establish quenched CLT's for linear and nonlinear random fields with independent innovations."]]></description>
<dc:subject>to:NB stochastic_processes random_fields martingales central_limit_theorem</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:138affc41fd1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:martingales"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.03238">
    <title>[1909.03238] Linear response and moderate deviations: hierarchical approach. V</title>
    <dc:date>2019-09-15T14:29:24+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.03238</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for some planary random fields of the form Xt=ψ(Gt) obtained from a Gaussian random field Gt via a function ψ, and consequently, for zeroes of the Gaussian Entire Function."]]></description>
<dc:subject>to:NB central_limit_theorem random_fields stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b61503a99002/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.09177">
    <title>[1908.09177] Dynamics of Stochastic Reaction-Diffusion Equations</title>
    <dc:date>2019-08-27T15:30:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.09177</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for SPDEs, which is always a challenge due to the irregularity of the noise terms that perturb the equation. In applications, such noise terms can quantify the lack of knowledge of certain parameters, finite-size effects, and/or fluctuations occurring due to external perturbations. Since SPDEs have become a key modelling tool in applications, there has been a growing interest in studying their dynamical phenomena. The main goal of this work is to provide a survey on different approaches to solution theory and dynamical properties for SPDEs, which is accessible for a wide community interested in modern methods in stochastic analysis, dynamics and applications."]]></description>
<dc:subject>to:NB stochastic_differential_equations random_fields stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d144e176a371/</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:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1810.04496">
    <title>[1810.04496] On maxima of stationary fields</title>
    <dc:date>2019-08-20T14:52:31+00:00</dc:date>
    <link>https://arxiv.org/abs/1810.04496</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Let {Xn:n∈ℤd} be a weakly dependent stationary field with maxima MA:=sup{Xi:i∈A} for finite A⊂ℤd and Mn:=sup{Xi:1≤i≤n} for n∈ℕd. In a general setting we prove that P(M(n,n,…,n)≤vn)=exp(−ndP(X0>vn,MAn≤vn))+o(1), for some increasing sequence of sets An of size o(nd). For a class of fields satisfying a local mixing condition, including m-dependent ones, the theorem holds with a constant finite A replacing An. The above results lead to new formulas for the extremal index for random fields."]]></description>
<dc:subject>to:NB extreme_values random_fields stochastic_processes mixing re:almost_none</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b48b11d4a911/</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:extreme_values"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1907.05414">
    <title>[1907.05414] Variational principle for weakly dependent random fields</title>
    <dc:date>2019-08-05T13:12:22+00:00</dc:date>
    <link>https://arxiv.org/abs/1907.05414</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis, Pfister, and Sullivan. The framework is then applied to derive the variational principle for the loop O(n) model and the Ising model in a random percolation environment in the nonmagnetic phase, and we explain how to extend the variational principle to similar models. To demonstrate the generality of the framework, we indicate how to naturally fit into it the variational principle for models with an absolutely summable interaction potential, and for the random-cluster model."]]></description>
<dc:subject>to:NB information_theory random_fields stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:83c995311f8f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1905.12554">
    <title>[1905.12554] Extreme value theory of evolving phenomena in complex dynamical systems: firing cascades in a model of neural network</title>
    <dc:date>2019-05-30T16:06:44+00:00</dc:date>
    <link>https://arxiv.org/abs/1905.12554</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individual subsystems linked by a network of interactions. As a specific example of the general theory, a model of neural network, introduced to describe the electrical activity of the cerebral cortex, is analyzed in detail: on the basis of this analysis we propose a novel definition of neuronal cascade, a physiological phenomenon of primary importance. We derive extreme value laws for the statistics of these cascades, both from the point of view of exceedances (that satisfy critical scaling theory) and of block maxima."]]></description>
<dc:subject>to:NB extreme_values random_fields dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1601c5f7fe9b/</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:extreme_values"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-conmatphys-033117-054252">
    <title>The Fokker–Planck Approach to Complex Spatiotemporal Disordered Systems | Annual Review of Condensed Matter Physics</title>
    <dc:date>2019-05-26T17:57:18+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-conmatphys-033117-054252</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real world, we need a top-down approach to complexity. In this approach, one may desire to understand general multipoint statistics. Here, such a general approach is presented and discussed based on examples from turbulence and sea waves. Our main idea is based on the cascade picture of turbulence, entangling fluctuations from large to small scales. Inspired by this cascade picture, we express the general multipoint statistics by the statistics of scale-dependent fluctuations of variables and relate it to a scale-dependent process, which finally is a stochastic cascade process. We show how to extract from empirical data a Fokker–Planck equation for this cascade process, which allows the generation of surrogate data to forecast extreme events as well as to develop a nonequilibrium thermodynamics for the complex systems. For each cascade event, an entropy production can be determined. These entropies accurately fulfill a rigorous law, namely the integral fluctuations theorem."

]]></description>
<dc:subject>to:NB stochastic_processes random_fields physics statistical_mechanics markov_models macro_from_micro non-equilibrium to_read color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:302abad9e4e5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macro_from_micro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-equilibrium"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.bj/1551862848">
    <title>Lee , Song : Stable limit theorems for empirical processes under conditional neighborhood dependence</title>
    <dc:date>2019-05-25T03:01:30+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.bj/1551862848</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets are indexed by the same set endowed with a neighborhood system. When the set of random variables satisfies CND, any two non-adjacent sets of random variables are conditionally independent given sigma algebras having indices in one of the two sets’ neighborhood. Random variables with CND include those with conditional dependency graphs and a class of Markov random fields with a global Markov property. The CND property is useful for modeling cross-sectional dependence governed by a complex, large network. This paper provides two main results. The first result is a stable central limit theorem for a sum of random variables with CND. The second result is a Donsker-type result of stable convergence of empirical processes indexed by a class of functions satisfying a certain bracketing entropy condition when the random variables satisfy CND."]]></description>
<dc:subject>to_read empirical_processes random_fields stochastic_processes central_limit_theorem in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f93b70f7625b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/book/10.1002/9781118720608">
    <title>Extremes in Random Fields | Wiley Series in Probability and Statistics</title>
    <dc:date>2019-01-07T17:50:30+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/book/10.1002/9781118720608</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Modern science typically involves the analysis of increasingly complex data. The extreme values that emerge in the statistical analysis of complex data are often of particular interest. This book focuses on the analytical approximations of the statistical significance of extreme values. Several relatively complex applications of the technique to problems that emerge in practical situations are presented.  All the examples are difficult to analyze using classical methods, and as a result, the author presents a novel technique, designed to be more accessible to the user.
"Extreme value analysis is widely applied in areas such as operational research, bioinformatics, computer science, finance and many other disciplines. This book will be useful for scientists, engineers and advanced graduate students who need to develop their own statistical tools for the analysis of their data. Whilst this book may not provide the reader with the specific answer it will inspire them to rethink their problem in the context of random fields, apply the method, and produce a solution."]]></description>
<dc:subject>books:noted downloaded random_fields stochastic_processes extreme_values statistics spatial_statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e3b27f839d2c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:extreme_values"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_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/1808.04739">
    <title>[1808.04739] Simulating Markov random fields with a conclique-based Gibbs sampler</title>
    <dc:date>2018-12-01T13:37:31+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.04739</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. At issue, fast simulation from such MRF models is often an important consideration, particularly when repeated generation of large numbers of data sets is required (e.g., for approximating sampling distributions). However, a standard Gibbs strategy for simulating from MRF models involves single-updates, performed with the conditional distribution of each observation in a sequential manner, whereby a Gibbs iteration may become computationally involved even for relatively small samples. As an alternative, we describe a general way to simulate from MRF models using Gibbs sampling with "concliques" (i.e., groups of non-neighboring observations). Compared to standard Gibbs sampling, this simulation scheme can be much faster by reducing Gibbs steps and by independently updating all observations per conclique at once. We detail the simulation method, establish its validity, and assess its computational performance through numerical studies, where speed advantages are shown for several spatial and network examples."

--- Slides: http://andeekaplan.com/phd-thesis/slides/public.pdf
--- There's an R package on Github but I couldn't get it to compile...]]></description>
<dc:subject>random_fields simulation stochastic_processes spatial_statistics network_data_analysis markov_models statistics computational_statistics to_teach:data_over_space_and_time have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:71d8eed500a5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<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:computational_statistics"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/0506080">
    <title>[math/0506080] Two new Markov order estimators</title>
    <dc:date>2018-09-23T22:17:23+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0506080</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present two new methods for estimating the order (memory depth) of a finite alphabet Markov chain from observation of a sample path. One method is based on entropy estimation via recurrence times of patterns, and the other relies on a comparison of empirical conditional probabilities. The key to both methods is a qualitative change that occurs when a parameter (a candidate for the order) passes the true order. We also present extensions to order estimation for Markov random fields."]]></description>
<dc:subject>in_NB markov_models statistical_inference_for_stochastic_processes model_selection recurrence_times entropy_estimation information_theory stochastic_processes have_read have_talked_about random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9585ed556542/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:recurrence_times"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_talked_about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1176348259">
    <title>Thomas-Agnan : Spline Functions and Stochastic Filtering</title>
    <dc:date>2016-04-16T15:13:50+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1176348259</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Some relationships have been established between unbiased linear predictors of processes, in signal and noise models, minimizing the predictive mean square error and some smoothing spline functions. We construct a new family of multidimensional splines adapted to the prediction of locally homogeneous random fields, whose "m-spectral measure" (to be defined) is absolutely continuous with respect to Lebesgue measure and satisfies some minor assumptions. By considering partial splines, one may include an arbitrary drift in the signal. This type of correspondence underlines the potentialities of cross-fertilization between statistics and the numerical techniques in approximation theory."]]></description>
<dc:subject>to:NB splines prediction filtering statistics hilbert_space fourier_analysis random_fields have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f733830bbdcd/</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:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fourier_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://infostructuralist.wordpress.com/2014/05/03/information-flow-on-graphs/">
    <title>Information flow on graphs | The Information Structuralist</title>
    <dc:date>2015-05-20T16:00:24+00:00</dc:date>
    <link>https://infostructuralist.wordpress.com/2014/05/03/information-flow-on-graphs/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[That's a very nice sufficient condition for a cellular automaton to be mixing --- actually it'd work for any Markov random field on a graph...]]></description>
<dc:subject>information_theory cellular_automata stochastic_processes mixing random_fields markov_models to:blog</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:270fa18b9ed2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cellular_automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.org/proceedings/papers/v33/liu14.html">
    <title>Learning Heterogeneous Hidden Markov Random Fields | AISTATS 2014 | JMLR W&amp;CP</title>
    <dc:date>2014-04-20T17:46:32+00:00</dc:date>
    <link>http://jmlr.org/proceedings/papers/v33/liu14.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Hidden Markov random fields (HMRFs) are conventionally assumed to be homogeneous in the sense that the potential functions are invariant across different sites. However in some biological applications, it is desirable to make HMRFs heterogeneous, especially when there exists some background knowledge about how the potential functions vary. We formally define heterogeneous HMRFs and propose an EM algorithm whose M-step combines a contrastive divergence learner with a kernel smoothing step to incorporate the background knowledge. Simulations show that our algorithm is effective for learning heterogeneous HMRFs and outperforms alternative binning methods. We learn a heterogeneous HMRF in a real-world study."

- It seems to me that heterogeneity (in this sense) is always a second-best modeling strategy to actually accounting for the variation using improved covariates, but...]]></description>
<dc:subject>to:NB markov_models random_fields statistics computational_statistics em_algorithm</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:082c1582939f/</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:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:em_algorithm"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://papers.nips.cc/paper/5154-conditional-random-fields-via-univariate-exponential-families">
    <title>Conditional Random Fields via Univariate Exponential Families</title>
    <dc:date>2014-01-04T03:34:39+00:00</dc:date>
    <link>http://papers.nips.cc/paper/5154-conditional-random-fields-via-univariate-exponential-families</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Conditional random fields, which model the distribution of a multivariate response conditioned on a set of covariates using undirected graphs, are widely used in a variety of multivariate prediction applications. Popular instances of this class of models such as categorical-discrete CRFs, Ising CRFs, and conditional Gaussian based CRFs, are not however best suited to the varied types of response variables in many applications, including count-valued responses. We thus introduce a “novel subclass of CRFs”, derived by imposing node-wise conditional distributions of response variables conditioned on the rest of the responses and the covariates as arising from univariate exponential families. This allows us to derive novel multivariate CRFs given any univariate exponential distribution, including the Poisson, negative binomial, and exponential distributions. Also in particular, it addresses the common CRF problem of specifying feature'' functions determining the interactions between response variables and covariates. We develop a class of tractable penalized M-estimators to learn these CRF distributions from data, as well as a unified sparsistency analysis for this general class of CRFs showing exact structure recovery can be achieved with high probability."]]></description>
<dc:subject>random_fields exponential_families graphical_models statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2dedac961c9a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<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="http://arxiv.org/abs/1104.3074">
    <title>[1104.3074] Consistency of the mean and the principal components of spatially distributed functional data</title>
    <dc:date>2013-12-14T16:35:51+00:00</dc:date>
    <link>http://arxiv.org/abs/1104.3074</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves X(sk;t),t∈[0,T], observed at spatial points s1,s2,…,sN. We establish conditions for the sample average (in space) of the X(sk) to be a consistent estimator of the population mean function, and for the usual empirical covariance operator to be a consistent estimator of the population covariance operator. These conditions involve an interplay of the assumptions on an appropriately defined dependence between the functions X(sk) and the assumptions on the spatial distribution of the points sk. The rates of convergence may be the same as for i.i.d. functional samples, but generally depend on the strength of dependence and appropriately quantified distances between the points sk. We also formulate conditions for the lack of consistency."]]></description>
<dc:subject>to:NB functional_data_analysis spatial_statistics random_fields statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e1498546eaf2/</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:functional_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1310.2646">
    <title>[1310.2646] Localized Iterative Methods for Interpolation in Graph Structured Data</title>
    <dc:date>2013-10-17T13:08:52+00:00</dc:date>
    <link>http://arxiv.org/abs/1310.2646</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on reconstructing bandlimited graph signals from partially observed samples. The iterative graph filtering approach very closely approximates the solution proposed in the that work, while being computationally more efficient. As an alternative, we propose a regularization based framework in which we define the cost of reconstruction to be a combination of smoothness of the graph signal and the reconstruction error with respect to the known samples, and find solutions that minimize this cost. We provide both a closed form solution and a computationally efficient iterative solution of the optimization problem. The experimental results on the recommendation system datasets demonstrate effectiveness of the proposed methods."]]></description>
<dc:subject>smoothing random_fields network_data_analysis re:small-area_estimation_by_smoothing in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:914379738cc4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:small-area_estimation_by_smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1308.6342">
    <title>[1308.6342] Efficient Learning of Practical Markov Random Fields with Exact Inference</title>
    <dc:date>2013-10-12T00:13:31+00:00</dc:date>
    <link>http://arxiv.org/abs/1308.6342</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a new parameter learning algorithm for a large class of Markov Random Fields (MRFs) with exact and efficient inference. Let the 1-neighbourhood of a parameterized clique be the union of the variables in the clique and in all the neighbour cliques. Then, the complexity of the inference step in the new learning algorithm, which we call LAP, is linear in the size of the MRF and exponential in the size of the 1-neighbourhood. In contrast, when using the junction tree algorithm for inference, the complexity is exponential in the tree-width of the MRF. Consequently, for a J by J square-lattice MRF, the complexity of an exact inference step with the junction tree algorithm is exponential in J, but it is only linear in J when using LAP. We prove that for individually parameterized cliques, the LAP and maximum likelihood estimates coincide. The LAP algorithm is natively parallel and hence ideal for massive-scale data modeling. The algorithm applies to many practical MRFs of great interest, including 2D and 3D lattices, chimera models, and skip-chain conditional random fields."]]></description>
<dc:subject>to:NB markov_models random_fields graphical_models computational_statistics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bfee5037fd1b/</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:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.6702">
    <title>[1309.6702] Statistical paleoclimate reconstructions via Markov random fields</title>
    <dc:date>2013-09-27T16:45:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.6702</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Understanding centennial scale climate variability requires datasets that are accurate, long, continuous, and of broad spatial coverage. Since instrumental measurements are generally only available after 1850, temperature fields must be reconstructed using paleoclimate archives, known as proxies. Various climate field reconstructions (CFR) methods have been proposed to relate past temperature and multiproxy networks, most notably the regularized EM algorithm (RegEM). In this work, we propose a new CFR method, called GraphEM, based on Gaussian Markov random fields (GMRF) embedded within RegEM. GMRFs provide a natural and flexible framework for modeling the inherent spatial heterogeneities of high-dimensional spatial fields, which would in general be more difficult with standard parametric covariance models. At the same time, they provide the parameter reduction necessary for obtaining precise and well-conditioned estimates of the covariance structure of the field, even when the sample size is much smaller than the number of variables (as is typically the case in paleoclimate applications). We demonstrate how the graphical structure of the field can be estimated from the data via l1-penalization methods, and how the GraphEM algorithm can be used to reconstruct past climate variations. The performance of GraphEM is then compared to a popular CFR method (RegEM TTLS) using synthetic data. Our results show that GraphEM can yield significant improvements over existing methods, with gains uniformly over space, and far better risk properties. We proceed to demonstrate that the increase in performance is directly related to recovering the underlying sparsity in the covariance of the spatial field. In particular, we show that spatial points with fewer neighbors in the recovered graph tend to be the ones where there are higher improvements in the reconstructions."]]></description>
<dc:subject>to:NB climatology variance_estimation random_fields sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:77aa4d790174/</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:climatology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variance_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<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="http://link.springer.com/article/10.1007/s10994-013-5399-7">
    <title>Spatio-temporal random fields: compressible representation and distributed estimation - Springer</title>
    <dc:date>2013-08-17T19:02:53+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/s10994-013-5399-7</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Modern sensing technology allows us enhanced monitoring of dynamic activities in business, traffic, and home, just to name a few. The increasing amount of sensor measurements, however, brings us the challenge for efficient data analysis. This is especially true when sensing targets can interoperate—in such cases we need learning models that can capture the relations of sensors, possibly without collecting or exchanging all data. Generative graphical models namely the Markov random fields (MRF) fit this purpose, which can represent complex spatial and temporal relations among sensors, producing interpretable answers in terms of probability. The only drawback will be the cost for inference, storing and optimizing a very large number of parameters—not uncommon when we apply them for real-world applications.
"In this paper, we investigate how we can make discrete probabilistic graphical models practical for predicting sensor states in a spatio-temporal setting. A set of new ideas allows keeping the advantages of such models while achieving scalability. We first introduce a novel alternative to represent model parameters, which enables us to compress the parameter storage by removing uninformative parameters in a systematic way. For finding the best parameters via maximum likelihood estimation, we provide a separable optimization algorithm that can be performed independently in parallel in each graph node. We illustrate that the prediction quality of our suggested method is comparable to those of the standard MRF and a spatio-temporal k-nearest neighbor method, while using much less computational resources."]]></description>
<dc:subject>random_fields graphical_models computational_statistics spatio-temporal_statistics to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:67cf1987c635/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1109.2694">
    <title>[1109.2694] Kernel density estimation for stationary random fields</title>
    <dc:date>2013-07-29T19:57:46+00:00</dc:date>
    <link>http://arxiv.org/abs/1109.2694</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, under natural and easily verifiable conditions, we prove the $\mathbb{L}^1$-convergence and the asymptotic normality of the Parzen-Rosenblatt density estimator for stationary random fields of the form $X_k = g(\varepsilon_{k-s}, s \in \Z^d)$, $k\in\Z^d$, where $(\varepsilon_i)_{i\in\Z^d}$ are i.i.d real random variables and $g$ is a measurable function defined on $\R^{\Z^d}$. Such kind of processes provides a general framework for stationary ergodic random fields. A Berry-Esseen's type central limit theorem is also given for the considered estimator."]]></description>
<dc:subject>to:NB density_estimation statistics random_fields mixing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5d228c8d75c8/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1307.3617">
    <title>[1307.3617] MCMC Learning</title>
    <dc:date>2013-07-16T16:53:40+00:00</dc:date>
    <link>http://arxiv.org/abs/1307.3617</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The theory of learning under the uniform distribution is rich and deep. It is connected to cryptography, computational complexity, and analysis of boolean functions to name a few areas. This theory however is very limited in applications due to the fact that the uniform distribution and the corresponding Fourier basis is rarely encountered as a statistical model. 
"A family of distributions that vastly generalizes the uniform distribution on the Boolean cube is that of distributions represented by Markov Random Fields (MRF). Markov Random Fields are one of the main tools for modeling high dimensional data in all areas of statistics and machine learning. 
"In this paper we initiate the investigation of extending central ideas, methods and algorithms from the theory of learning under the uniform distribution to the setup of learning concepts given examples from MRF distributions. In particular, our results establish a novel connection between properties of MCMC sampling of MRFs and learning under the MRF distribution."]]></description>
<dc:subject>to:NB learning_theory markov_models random_fields mossel.elchanan</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d9fe83eeda3c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mossel.elchanan"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1307.1379">
    <title>[1307.1379] Multivariate Gaussian Random Fields Using Systems of Stochastic Partial Differential Equations</title>
    <dc:date>2013-07-08T16:34:41+00:00</dc:date>
    <link>http://arxiv.org/abs/1307.1379</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduced and applied to simulated data and real data. By solving a system of SPDEs, we can construct multivariate GRFs. On the theoretical side, the notorious requirement of non-negative definiteness for the covariance matrix of the GRF is satisfied since the constructed covariance matrices with this approach are automatically symmetric positive definite. Using the approximate stochastic weak solutions to the systems of SPDEs, multivariate GRFs are represented by multivariate Gaussian \emph{Markov} random fields (GMRFs) with sparse precision matrices. Therefore, on the computational side, the sparse structures make it possible to use numerical algorithms for sparse matrices to do fast sampling from the random fields and statistical inference. Therefore, the \emph{big-n} problem can also be partially resolved for these models. These models out-preform existing multivariate GRF models on a commonly used real dataset."]]></description>
<dc:subject>computational_statistics random_fields stochastic_differential_equations stochastic_processes spatial_statistics statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e9d946472b64/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<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:spatial_statistics"/>
	<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="http://arxiv.org/abs/1307.1565">
    <title>[1307.1565] Concentration inequalities for smooth random fields</title>
    <dc:date>2013-07-08T16:32:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1307.1565</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some deterministic point plus an intrinsic dimension of the optimisation problem. As an application we prove the exponential inequality for a function of the maximal eigenvalue of a random matrix is proved."]]></description>
<dc:subject>random_fields empirical_processes concentration_of_measure stochastic_processes re:almost_none in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:145934415469/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:concentration_of_measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:almost_none"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1306.6205">
    <title>[1306.6205] Extrapolation of Stationary Random Fields</title>
    <dc:date>2013-06-27T15:27:07+00:00</dc:date>
    <link>http://arxiv.org/abs/1306.6205</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non--Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging."]]></description>
<dc:subject>spatial_statistics prediction random_fields statistics to_teach:data_over_space_and_time in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:277890bb07ee/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aoas/1372338484">
    <title>Forbes , Charras-Garrido , Azizi , Doyle , Abrial : Spatial risk mapping for rare disease with hidden Markov fields and variational EM</title>
    <dc:date>2013-06-27T15:09:18+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aoas/1372338484</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Current risk mapping models for pooled data focus on the estimated risk for each geographical unit. A risk classification, that is, grouping of geographical units with similar risk, is then necessary to easily draw interpretable maps, with clearly delimited zones in which protection measures can be applied. As an illustration, we focus on the Bovine Spongiform Encephalopathy (BSE) disease that threatened the bovine production in Europe and generated drastic cow culling. This example features typical animal disease risk analysis issues with very low risk values, small numbers of observed cases and population sizes that increase the difficulty of an automatic classification. We propose to handle this task in a spatial clustering framework using a nonstandard discrete hidden Markov model prior designed to favor a smooth risk variation. The model parameters are estimated using an EM algorithm and a mean field approximation for which we develop a new initialization strategy appropriate for spatial Poisson mixtures. Using both simulated and our BSE data, we show that our strategy performs well in dealing with low population sizes and accurately determines high risk regions, both in terms of localization and risk level estimation."

--- Why not just use an L1 penalty on estimated risk levels?]]></description>
<dc:subject>spatial_statistics estimation epidemiology random_fields markov_models statistics have_read in_NB re:small-area_estimation_by_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3a64f128c707/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:epidemiology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<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:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:small-area_estimation_by_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1306.2295">
    <title>[1306.2295] Markov random fields factorization with context-specific independences</title>
    <dc:date>2013-06-12T20:00:42+00:00</dc:date>
    <link>http://arxiv.org/abs/1306.2295</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to factorize a Gibbs distribution into a set of factors. However, an important issue of using a graph to represent independences is that it cannot encode some types of independence relations, such as the context-specific independences (CSIs). They are a particular case of conditional independences that is true only for a certain assignment of its conditioning set; in contrast to conditional independences that must hold for all its assignments. This work presents a method for factorizing a Markov random field according to CSIs present in a distribution, and formally guarantees that this factorization is correct. This is presented in our main contribution, the context-specific Hammersley-Clifford theorem, a generalization to CSIs of the Hammersley-Clifford theorem that applies for conditional independences."]]></description>
<dc:subject>to:NB markov_models random_fields graphical_models probability</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b020f03d8c26/</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:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1302.5616">
    <title>[1302.5616] Large Deviations for Nonlocal Stochastic Neural Fields</title>
    <dc:date>2013-03-27T14:10:59+00:00</dc:date>
    <link>http://arxiv.org/abs/1302.5616</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a $Q$-Wiener process and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substanial difficulties but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multi-scale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations."]]></description>
<dc:subject>random_fields neural_networks stochastic_differential_equations large_deviations in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8572f1a4cc5e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://onlinelibrary.wiley.com/doi/10.1002/sjos.12000/abstract">
    <title>Lévy-based Modelling in Brain Imaging - JÓNSDÓTTIR - 2013 - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2013-02-23T17:43:07+00:00</dc:date>
    <link>http://onlinelibrary.wiley.com/doi/10.1002/sjos.12000/abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A substantive problem in neuroscience is the lack of valid statistical methods for non-Gaussian random fields. In the present study, we develop a flexible, yet tractable model for a random field based on kernel smoothing of a so-called Lévy basis. The resulting field may be Gaussian, but there are many other possibilities, including random fields based on Gamma, inverse Gaussian and normal inverse Gaussian (NIG) Lévy bases. It is easy to estimate the parameters of the model and accordingly to assess by simulation the quantiles of test statistics commonly used in neuroscience. We give a concrete example of magnetic resonance imaging scans that are non-Gaussian. For these data, simulations under the fitted models show that traditional methods based on Gaussian random field theory may leave small, but significant changes in signal level undetected, while these changes are detectable under a non-Gaussian Lévy model."]]></description>
<dc:subject>to:NB neuroscience fmri random_fields spatial_statistics levy_processes cumulants</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5864833c3e57/</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:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fmri"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:levy_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cumulants"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/chapter/10.1007%2F978-3-642-33305-7_10">
    <title>Central Limit Theorems for Weakly Dependent Random Fields - Springer</title>
    <dc:date>2013-02-12T01:43:44+00:00</dc:date>
    <link>http://link.springer.com/chapter/10.1007%2F978-3-642-33305-7_10</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This chapter is a primer on the limit theorems for dependent random fields. First, dependence concepts such as mixing, association and their generalizations are introduced. Then, moment inequalities for sums of dependent random variables are stated which yield e.g. the asymptotic behaviour of the variance of these sums which is essential for the proof of limit theorems. Finally, central limit theorems for dependent random fields are given. Applications to excursion sets of random fields and Newman’s conjecture in the absence of finite susceptibility are discussed as well."]]></description>
<dc:subject>to:NB central_limit_theorem stochastic_processes mixing random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d234ea141b38/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mixing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007/s00184-011-0374-4">
    <title>Kernel spatial density estimation in infinite dimension space - Springer</title>
    <dc:date>2013-01-07T04:08:23+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/s00184-011-0374-4</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we propose a nonparametric method to estimate the spatial density of a functional stationary random field. This latter is with values in some infinite dimensional normed space and admitted a density with respect to some reference measure. We study both the weak and strong consistencies of the considered estimator and also give some rates of convergence. Special attention is paid to the links between the probabilities of small balls and the rates of convergence of the estimator. The practical use and the behavior of the estimator are illustrated through some simulations and a real data application."]]></description>
<dc:subject>to:NB density_estimation statistics random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:34626e06fe83/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.nowpublishers.com/product.aspx?product=MAL&amp;doi=2200000013">
    <title>An Introduction to Conditional Random Fields</title>
    <dc:date>2012-08-23T17:57:40+00:00</dc:date>
    <link>http://www.nowpublishers.com/product.aspx?product=MAL&amp;doi=2200000013</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many tasks involve predicting a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling. They combine the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. This survey describes conditional random fields, a popular probabilistic method for structured prediction. CRFs have seen wide application in many areas, including natural language processing, computer vision, and bioinformatics. We describe methods for inference and parameter estimation for CRFs, including practical issues for implementing large-scale CRFs. We do not assume previous knowledge of graphical modeling, so this survey is intended to be useful to practitioners in a wide variety of fields."]]></description>
<dc:subject>to:NB random_fields graphical_models machine_learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e08017fb2e76/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1206.2303">
    <title>[1206.2303] Population oscillations in spatial stochastic Lotka-Volterra models: A field-theoretic perturbational analysis</title>
    <dc:date>2012-06-23T15:15:04+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.2303</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is characterized by neutral cycles in phase space, describing undamped oscillations for both predator and prey populations. In contrast, Monte Carlo simulations for stochastic two-species predator-prey reaction systems on regular lattices display complex spatio-temporal structures associated with persistent erratic population oscillations. The Doi-Peliti path integral representation of the master equation for stochastic particle interaction models is utilized to arrive at a field theory action for spatial Lotka-Volterra models in the continuum limit. In the species coexistence phase, a perturbation expansion with respect to the nonlinear predation rate is employed to demonstrate that spatial degrees of freedom and stochastic noise induce instabilities toward structure formation, and to compute the fluctuation corrections for the oscillation frequency and diffusion coefficient. The drastic downward renormalization of the frequency and the enhanced diffusivity are in excellent qualitative agreement with Monte Carlo simulation data."]]></description>
<dc:subject>to:NB lotka-volterra ecology field_theory stochastic_processes random_fields</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5add7359e10c/</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:lotka-volterra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ecology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:field_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1206.3985">
    <title>[1206.3985] Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models</title>
    <dc:date>2012-06-19T14:33:48+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.3985</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper addresses the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. This bound depends on the derivatives of a likelihood distribution that is generally intractable. It is established that by exploiting a property of the exponential family, this intractable bound can be related to the statistical moments of the Gibbs potential of the Markov random field. A derivative-free Monte Carlo algorithm is then proposed to estimate this moments and compute the bound. To illustrate the interest of this method, the proposed algorithm is successfully applied to the Ising and Potts models. The resulting bounds are used to assess the performance of three state-of-the art estimators of the parameter of these Markov random fields."]]></description>
<dc:subject>spatial_statistics random_fields markov_models fisher_information exponential_families statistics in_NB cramer-rao_inequality</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8d34c4c6630e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fisher_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cramer-rao_inequality"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1206.2398">
    <title>[1206.2398] LICORS: Light Cone Reconstruction of States for Non-parametric Forecasting of Spatio-Temporal Systems</title>
    <dc:date>2012-06-17T22:57:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.2398</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[We present a new non-parametric forecasting method for data where continuous values are observed on a regular spatial grid at regular time-intervals. Our method, "light-cone reconstruction of causal states" (LICORS), uses physical principles to identify predictive states which are local properties of the system, both in space and time. LICORS is completely non-parametric, discovering the number of predictive states and their predictive distributions automatically, and consistently under mild assumptions on the data-generating process. We provide an algorithm to implement our method, along with a cross-validation scheme to pick control settings. Simulations show that CV-tuned LICORS outperforms standard time series methods in forecasting challenging spatio-temporal dynamics. Our work thus provides applied researchers with a new, highly automatic method to analyze and optimally forecast spatio-temporal data.]]></description>
<dc:subject>self-promotion to:blog prediction statistics random_fields spatial_statistics dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c64ad2eb72f9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-promotion"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:blog"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>