Advanced Markov Chain Monte Carlo Methods - Learning From Past Samples

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...

List of contents

Preface.
 
Acknowledgments.
 
Publisher's Acknowledgments.
 
1 Bayesian Inference and Markov Chain Monte Carlo.
 
1.1 Bayes.
 
1.1.1 Specification of Bayesian Models.
 
1.1.2 The Jeffreys Priors and Beyond.
 
1.2 Bayes Output.
 
1.2.1 Credible Intervals and Regions.
 
1.2.2 Hypothesis Testing: Bayes Factors.
 
1.3 Monte Carlo Integration.
 
1.3.1 The Problem.
 
1.3.2 Monte Carlo Approximation.
 
1.3.3 Monte Carlo via Importance Sampling.
 
1.4 Random Variable Generation.
 
1.4.1 Direct or TransformationMethods.
 
1.4.2 Acceptance-Rejection Methods.
 
1.4.3 The Ratio-of-UniformsMethod and Beyond.
 
1.4.4 Adaptive Rejection Sampling.
 
1.4.5 Perfect Sampling.
 
1.5 Markov ChainMonte Carlo.
 
1.5.1 Markov Chains.
 
1.5.2 Convergence Results.
 
1.5.3 Convergence Diagnostics.
 
Exercises.
 
2 The Gibbs Sampler.
 
2.1 The Gibbs Sampler.
 
2.2 Data Augmentation.
 
2.3 Implementation Strategies and Acceleration Methods.
 
2.3.1 Blocking and Collapsing.
 
2.3.2 Hierarchical Centering and Reparameterization.
 
2.3.3 Parameter Expansion for Data Augmentation.
 
2.3.4 Alternating Subspace-Spanning Resampling.
 
2.4 Applications.
 
2.4.1 The Student-tModel.
 
2.4.2 Robit Regression or Binary Regression with the Student-t Link.
 
2.4.3 Linear Regression with Interval-Censored Responses.
 
Exercises.
 
Appendix 2A: The EMand PX-EMAlgorithms.
 
3 The Metropolis-Hastings Algorithm.
 
3.1 TheMetropolis-Hastings Algorithm.
 
3.1.1 Independence Sampler.
 
3.1.2 RandomWalk Chains.
 
3.1.3 Problems withMetropolis-Hastings Simulations.
 
3.2 Variants of theMetropolis-Hastings Algorithm.
 
3.2.1 The Hit-and-Run Algorithm.
 
3.2.2 The Langevin Algorithm.
 
3.2.3 TheMultiple-TryMH Algorithm.
 
3.3 Reversible Jump MCMC Algorithm for Bayesian Model Selection Problems.
 
3.3.1 Reversible JumpMCMC Algorithm.
 
3.3.2 Change-Point Identification.
 
3.4 Metropolis-Within-Gibbs Sampler for ChIP-chip Data Analysis.
 
3.4.1 Metropolis-Within-Gibbs Sampler.
 
3.4.2 Bayesian Analysis for ChIP-chip Data.
 
Exercises.
 
4 Auxiliary Variable MCMC Methods.
 
4.1 Simulated Annealing.
 
4.2 Simulated Tempering.
 
4.3 The Slice Sampler.
 
4.4 The Swendsen-Wang Algorithm.
 
4.5 TheWolff Algorithm.
 
4.6 The Mo/ller Algorithm.
 
4.7 The Exchange Algorithm.
 
4.8 The DoubleMH Sampler.
 
4.8.1 Spatial AutologisticModels.
 
4.9 Monte CarloMH Sampler.
 
4.9.1 Monte CarloMH Algorithm.
 
4.9.2 Convergence.
 
4.9.3 Spatial AutologisticModels (Revisited).
 
4.9.4 Marginal Inference.
 
4.10 Applications.
 
4.10.1 AutonormalModels.
 
4.10.2 Social Networks.
 
Exercises.
 
5 Population-Based MCMC Methods.
 
5.1 Adaptive Direction Sampling.
 
5.2 Conjugate GradientMonte Carlo.
 
5.3 SampleMetropolis-Hastings Algorithm.
 
5.4 Parallel Tempering.
 
5.5 EvolutionaryMonte Carlo.
 
5.5.1 Evolutionary Monte Carlo in Binary-Coded Space.
 
5.5.2 EvolutionaryMonte Carlo in Continuous Space.
 
5.5.3 Implementation Issues.
 
5.5.4 Two Illustrative Examples.
 
5.5.5 Discussion.
 
5.6 Sequential Parallel Tempering for Simulation of High Dimensional Systems.
 
5.6.1 Buil

Report

"The book is suitable as a textbook for one-semester courses on Monte Carlo methods, offered at the advance postgraduate levels." ( Mathematical Reviews , 1 December 2012) "Researchers working in the field of applied statistics will profit from this easy-to-access presentation. Further illustration is done by discussing interesting examples and relevant applications. The valuable reference list includes technical reports which are hard to and by searching in public data bases." (Zentralblatt MATH, 2011) "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." (Breitbart.com: Business Wire , 1 February 2011) "The Markov Chain Monte Carlo method has now become the dominant methodology for solving many classes of computational problems in science and technology." (SciTech Book News, December 2010)

Product details

• Authors: Raymond Carroll, Raymond J. Carroll, Carroll Raymond, Liang, Famin Liang, Faming Liang, Faming Liu Liang, Liang Faming, LIANG FAMING LIU CHUANHAI CARROL, Chuanha Liu, Chuanhai Liu, Liu Chuanhai
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 16.07.2010
• EAN: 9780470748268
• ISBN: 978-0-470-74826-8
• No. of pages: 378
• Dimensions: 160 mm x 235 mm x 28 mm
• Series: Wiley Series in Computational Statistics; Wiley Series in Computational; Wiley Series in Computational Statistics
• Subjects: Education and learning > Teaching preparation > Vocational needs; Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Wahrscheinlichkeitsrechnung, Statistics, Bayes-Verfahren, Rechnergestützte u. graphische Statistik, Computational & Graphical Statistics, Bayesian Analysis