Advanced Markov Chain Monte Carlo Methods (eBook)

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.

Preface

Acknowledgements

List of Figures

List of Tables

1 Bayesian Inference and Markov chain Monte Carlo

1.1 Bayes

1.2 Bayes output

1.3 Monte Carlo Integration

1.4 Random variable generation

1.5 Markov chain Monte Carlo

Exercises

2 The Gibbs sampler

2.1 The Gibbs sampler

2.2 Data Augmentation

2.3 Implementation strategies and acceleration methods

2.4 Applications

Exercises

3 The Metropolis-Hastings Algorithm

3.1 The Metropolis-Hastings Algorithm

3.2 Some Variants of the Metropolis-Hastings Algorithm

3.3 Reversible Jump MCMC Algorithm for Bayesian Model Selection

Problems

3.4 Metropolis-within-Gibbs Sampler for ChIP-chip Data Analysis

Exercises

4 Auxiliary Variable MCMC Methods

4.1 Simulated Annealing

4.2 Simulated Tempering

4.3 Slice Sampler

4.4 The Swendsen-Wang Algorithm

4.5 The Wolff Algorithm

4.6 The Møller algorithm

4.7 The Exchange Algorithm

4.8 Double MH Sampler

4.9 Monte Carlo MH Sampler

4.10 Applications

Exercises

5 Population-Based MCMC Methods

5.1 Adaptive Direction Sampling

5.2 Conjugate Gradient Monte Carlo

5.3 Sample Metropolis-Hastings Algorithm

5.4 Parallel Tempering

5.5 Evolutionary Monte Carlo

5.6 Sequential Parallel Tempering for Simulation of High Dimensional

Systems

5.7 Equi-Energy Sampler

5.8 Applications

Forecasting

Exercises

6 Dynamic Weighting

6.1 Dynamic Weighting

6.2 Dynamically Weighted Importance Sampling

6.3 Monte Carlo Dynamically Weighted Importance Sampling

6.4 Sequentially Dynamically Weighted Importance Sampling

Exercises

7 Stochastic Approximation Monte Carlo

7.1 Multicanonical Monte Carlo

7.2 1/k-Ensemble Sampling

7.3 Wang-Landau Algorithm

7.4 Stochastic Approximation Monte Carlo

7.5 Applications of Stochastic Approximation Monte Carlo

7.6 Variants of Stochastic Approximation Monte Carlo

7.7 Theory of Stochastic Approximation Monte Carlo

7.8 Trajectory Averaging: Toward the Optimal Convergence Rate

Exercises

8 Markov Chain Monte Carlo with Adaptive Proposals

8.1 Stochastic Approximation-based Adaptive Algorithms

8.2 Adaptive Independent Metropolis-Hastings Algorithms

8.3 Regeneration-based Adaptive Algorithms

8.4 Population-based Adaptive Algorithms

Exercises

References

Index

"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)