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Informationen zum Autor Faming Liang, Associate Professor, Department of Statistics, Texas A&M University. Chuanhai Liu, Professor, Department of Statistics, Purdue University. Raymond J. Carroll, Distinguished Professor, Department of Statistics, Texas A&M University. Klappentext Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics.Key Features:* Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems.* A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants.* Up-to-date accounts of recent developments of the Gibbs sampler.* Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals.* Accompanied by a supporting website featuring datasets used in the book, along with codes used for some simulation examples.This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial. Zusammenfassung * Presents the latest developments in Monte Carlo research. * Provides a toolkit for simulating complex systems using MCMC. * Introduces a wide range of algorithms including Gibbs sampler, Metropolis-Hastings and an overview of sequential Monte Carlo algorithms. Inhaltsverzeichnis Preface xiii Acknowledgments xvii Publisher's Acknowledgments xix 1 Bayesian Inference and Markov Chain Monte Carlo 1 1.1 Bayes 1 1.1.1 Specification of Bayesian Models 2 1.1.2 The Jeffreys Priors and Beyond 2 1.2 Bayes Output 4 1.2.1 Credible Intervals and Regions 4 1.2.2 Hypothesis Testing: Bayes Factors 5 1.3 Monte Carlo Integration 8 1.3.1 The Problem 8 1.3.2 Monte Carlo Approximation 9 1.3.3 Monte Carlo via Importance Sampling 9 1.4 Random Variable Generation 10 1.4.1 Direct or Transformation Methods 1 1.4.2 Acceptance-Rejection Methods 11 1.4.3 The Ratio-of-Uniforms Method and Beyond 14 1.4.4 Adaptive Rejection Sampling 18 1.4.5 Perfect Sampling 18 1.5 Markov Chain Monte Carlo 18 1.5.1 Markov Chains 18 1.5.2 Convergence Results 20 1.5.3 Convergence Diagnostics 23 Exercises 24 2 The Gibbs Sampler 27 2.1 The Gibbs Sampler 27 2.2 Data Augmentation 30 2.3 Implementation Strategies and Acceleration Methods 33 2.3.1 Blocking and Collapsing 33 2.3.2 Hierarchical Centering and Reparameterization 34 2.3.3 Parameter Expansion for Data Augmentation 35 2.3.4 Alternating Subspace-Spanning Resampling 43 2.4 Applications 45 2.4.1 The Student-t Model 45 2.4.2 Robit Regression or Binary Regression with the Student-t Link 47 2.4.3 Linear Regression with Interval-Censored Responses 50 Exercises 54 Appendix 2A: The EM and PX-EM Algorithms 56 3 The Metropolis-Hastings Algorithm 59 3.1 The Metropolis-Hastings Algorithm 59 3.1.1 Independence Sampler 62 3.1.2 Random Walk Chains 63 3.1.3 Problems with Metropolis-Hastings Simulations 63 3.2 Variants of the Metropolis-Hastings Algorithm 65 3.2.1 The Hit-and-Run Algorithm. 65 3.2.2 The Langevin Algorithm 65 3.2.3 The Multiple-Try MH Algorithm 66 3.3 Reversible Jump MCMC...
