Advanced Markov Chain Monte Carlo Methods

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. 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.

Markov Chain Monte Carlo (MCMC) methods are now an indispensabletool in scientific computing. This book discusses recentdevelopments of MCMC methods with an emphasis on those making useof past sample information during simulations. The applicationexamples are drawn from diverse fields such as bioinformaticsmachine learning, social science, combinatorial optimization, andcomputational physics.Key Features:* Expanded coverage of the stochastic approximation Monte Carloand dynamic weighting algorithms that are essentially immune tolocal trap problems.* A detailed discussion of the Monte Carlo Metropolis-Hastingsalgorithm that can be used for sampling from distributions withintractable normalizing constants.* Up-to-date accounts of recent developments of the Gibbssampler.* Comprehensive overviews of the population-based MCMC algorithmsand the MCMC algorithms with adaptive proposals.This book can be used as a textbook or a reference book for aone-semester graduate course in statistics, computational biologyengineering, and computer sciences. Applied or theoreticalresearchers will also find this book beneficial.

PrefaceAcknowledgementsList of FiguresList of Tables1 Bayesian Inference and Markov chain Monte Carlo1.1 Bayes1.2 Bayes output1.3 Monte Carlo Integration1.4 Random variable generation1.5 Markov chain Monte CarloExercises2 The Gibbs sampler2.1 The Gibbs sampler2.2 Data Augmentation2.3 Implementation strategies and acceleration methods2.4 ApplicationsExercises3 The Metropolis-Hastings Algorithm3.1 The Metropolis-Hastings Algorithm3.2 Some Variants of the Metropolis-Hastings Algorithm3.3 Reversible Jump MCMC Algorithm for Bayesian Model SelectionProblems3.4 Metropolis-within-Gibbs Sampler for ChIP-chip Data AnalysisExercises4 Auxiliary Variable MCMC Methods4.1 Simulated Annealing4.2 Simulated Tempering4.3 Slice Sampler4.4 The Swendsen-Wang Algorithm4.5 The Wolff Algorithm4.6 The Møller algorithm4.7 The Exchange Algorithm4.8 Double MH Sampler4.9 Monte Carlo MH Sampler4.10 ApplicationsExercises5 Population-Based MCMC Methods5.1 Adaptive Direction Sampling5.2 Conjugate Gradient Monte Carlo5.3 Sample Metropolis-Hastings Algorithm5.4 Parallel Tempering5.5 Evolutionary Monte Carlo5.6 Sequential Parallel Tempering for Simulation of High DimensionalSystems5.7 Equi-Energy Sampler5.8 ApplicationsForecastingExercises6 Dynamic Weighting6.1 Dynamic Weighting6.2 Dynamically Weighted Importance Sampling6.3 Monte Carlo Dynamically Weighted Importance Sampling6.4 Sequentially Dynamically Weighted Importance SamplingExercises7 Stochastic Approximation Monte Carlo7.1 Multicanonical Monte Carlo7.2 1/k-Ensemble Sampling7.3 Wang-Landau Algorithm7.4 Stochastic Approximation Monte Carlo7.5 Applications of Stochastic Approximation Monte Carlo7.6 Variants of Stochastic Approximation Monte Carlo7.7 Theory of Stochastic Approximation Monte Carlo7.8 Trajectory Averaging: Toward the Optimal Convergence RateExercises8 Markov Chain Monte Carlo with Adaptive Proposals8.1 Stochastic Approximation-based Adaptive Algorithms8.2 Adaptive Independent Metropolis-Hastings Algorithms8.3 Regeneration-based Adaptive Algorithms8.4 Population-based Adaptive AlgorithmsExercisesReferencesIndex