Advanced markov chain monte carlo methods - learning from past samples

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.

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...