The Experts below are selected from a list of 154746 Experts worldwide ranked by ideXlab platform
Yan Liu - One of the best experts on this subject based on the ideXlab platform.
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a parallel evolutionary multiple try metropolis Markov Chain monte carlo algorithm for sampling spatial partitions
Statistics and Computing, 2021Co-Authors: Wendy Tam K Cho, Yan LiuAbstract:We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov Chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov Chains running in parallel.
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a parallel evolutionary multiple try metropolis Markov Chain monte carlo algorithm for sampling spatial partitions
arXiv: Computation, 2020Co-Authors: Wendy Tam K Cho, Yan LiuAbstract:We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov Chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hasting ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel architecture through the integration of a parallel EA framework that guides Markov Chains running in parallel.
Wendy Tam K Cho - One of the best experts on this subject based on the ideXlab platform.
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a parallel evolutionary multiple try metropolis Markov Chain monte carlo algorithm for sampling spatial partitions
Statistics and Computing, 2021Co-Authors: Wendy Tam K Cho, Yan LiuAbstract:We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov Chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov Chains running in parallel.
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a parallel evolutionary multiple try metropolis Markov Chain monte carlo algorithm for sampling spatial partitions
arXiv: Computation, 2020Co-Authors: Wendy Tam K Cho, Yan LiuAbstract:We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov Chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hasting ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel architecture through the integration of a parallel EA framework that guides Markov Chains running in parallel.
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understanding significance tests from a non mixing Markov Chain for partisan gerrymandering claims
Statistics and Public Policy, 2019Co-Authors: Wendy Tam K Cho, Simon RubinsteinsalzedoAbstract:ABSTRACTRecently, Chikina, Frieze, and Pegden proposed a way to assess significance in a Markov Chain without requiring that Markov Chain to mix. They presented their theorem as a rigorous test for...
Roman Holenstein - One of the best experts on this subject based on the ideXlab platform.
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particle Markov Chain monte carlo methods
Journal of The Royal Statistical Society Series B-statistical Methodology, 2010Co-Authors: Christophe Andrieu, Arnaud Doucet, Roman HolensteinAbstract:Markov Chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov Chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov Chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Levy-driven stochastic volatility model. Copyright (c) 2010 Royal Statistical Society.
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Particle Markov Chain Monte Carlo methods
Journal of the Royal Statistical Society Series B-Statistical Methodology, 2010Co-Authors: Christophe Andrieu, Arnaud Doucet, Roman HolensteinAbstract:Markov Chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov Chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov Chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Levy-driven stochastic volatility model.
Galin L. Jones - One of the best experts on this subject based on the ideXlab platform.
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Multivariate Output Analysis for Markov Chain Monte Carlo
arXiv: Statistics Theory, 2015Co-Authors: Dootika Vats, James M. Flegal, Galin L. JonesAbstract:Markov Chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities? The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov Chain central limit theorem (CLT). The multivariate nature of this Monte Carlo error largely has been ignored in the MCMC literature. We present a multivariate framework for terminating simulation in MCMC. We define a multivariate effective sample size, estimating which requires strongly consistent estimators of the covariance matrix in the Markov Chain CLT; a property we show for the multivariate batch means estimator. We then provide a lower bound on the number of minimum effective samples required for a desired level of precision. This lower bound depends on the problem only in the dimension of the expectation being estimated, and not on the underlying stochastic process. This result is obtained by drawing a connection between terminating simulation via effective sample size and terminating simulation using a relative standard deviation fixed-volume sequential stopping rule; which we demonstrate is an asymptotically valid procedure. The finite sample properties of the proposed method are demonstrated in a variety of examples.
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handbook of Markov Chain monte carlo
2011Co-Authors: Steve Brooks, Galin L. Jones, Andrew Gelman, Xiaoli MengAbstract:Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov Chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov Chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov Chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov Chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western
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Markov Chain monte carlo can we trust the third significant figure
arXiv: Statistics Theory, 2007Co-Authors: James M. Flegal, Murali Haran, Galin L. JonesAbstract:Current reporting of results based on Markov Chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov Chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.
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On the Markov Chain central limit theorem
Probability Surveys, 2004Co-Authors: Galin L. JonesAbstract:The goal of this expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov Chains. This is done with a view towards Markov Chain Monte Carlo settings and hence the focus is on the connections between drift and mixing conditions and their implications. In particular, we consider three commonly cited central limit theorems and discuss their relationship to classical results for mixing processes. Several motivating examples are given which range from toy one-dimensional settings to complicated settings encountered in Markov Chain Monte Carlo.
Christophe Andrieu - One of the best experts on this subject based on the ideXlab platform.
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particle Markov Chain monte carlo methods
Journal of The Royal Statistical Society Series B-statistical Methodology, 2010Co-Authors: Christophe Andrieu, Arnaud Doucet, Roman HolensteinAbstract:Markov Chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov Chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov Chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Levy-driven stochastic volatility model. Copyright (c) 2010 Royal Statistical Society.
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Particle Markov Chain Monte Carlo methods
Journal of the Royal Statistical Society Series B-Statistical Methodology, 2010Co-Authors: Christophe Andrieu, Arnaud Doucet, Roman HolensteinAbstract:Markov Chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov Chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov Chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Levy-driven stochastic volatility model.
