This book provides comprehensive coverage of simulation of complex systems using Monte Carlo methods. Developing algorithms that are immune to the local trap problem has long been considered as the most important topic in MCMC research. Various advanced MCMC algorithms which address this problem have been developed include, the modified Gibbs sampler, the methods based on auxiliary variables and the methods making use of past samples. The focus of this book is on the algorithms that make use of past samples. This book includes the multicanonical algorithm, dynamic weighting, dynamically weighted importance sampling, the Wang-Landau algorithm, equal energy sampler, stochastic approximation Monte Carlo, adaptive MCMC algorithms, conjugate gradient Monte Carlo, adaptive direction sampling, the sampling Metropolis-Hasting algorithm and the multiplica sampler.
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 Moller 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
