Preface |
Acknowledgements |
List of Figures |
List of Tables |
Bayesian Inference and Markov chain Monte Carlo / 1: |
Bayes / 1.1: |
Bayes output / 1.2: |
Monte Carlo Integration / 1.3: |
Random variable generation / 1.4: |
Markov chain Monte Carlo / 1.5: |
Exercises |
The Gibbs sampler / 2: |
Data Augmentation / 2.1: |
Implementation strategies and acceleration methods / 2.3: |
Applications / 2.4: |
The Metropolis-Hastings Algorithm / 3: |
Some Variants of the Metropolis-Hastings Algorithm / 3.1: |
Reversible Jump MCMC Algorithm for Bayesian Model Selection / 3.3: |
Problems |
Metropolis-within-Gibbs Sampler for ChIP-chip Data Analysis / 3.4: |
Auxiliary Variable MCMC Methods / 4: |
Simulated Annealing / 4.1: |
Simulated Tempering / 4.2: |
Slice Sampler / 4.3: |
The Swendsen-Wang Algorithm / 4.4: |
The Wolff Algorithm / 4.5: |
The Mller algorithm / 4.6: |
The Exchange Algorithm / 4.7: |
Double MH Sampler / 4.8: |
Monte Carlo MH Sampler / 4.9: |
Population-Based MCMC Methods / 4.10: |
Adaptive Direction Sampling / 5.1: |
Conjugate Gradient Monte Carlo / 5.2: |
Sample Metropolis-Hastings Algorithm / 5.3: |
Parallel Tempering / 5.4: |
Evolutionary Monte Carlo / 5.5: |
Sequential Parallel Tempering for Simulation of High Dimensional / 5.6: |
Systems |
Equi-Energy Sampler / 5.7: |
Forecasting / 5.8: |
Dynamic Weighting / 6: |
Dynamically Weighted Importance Sampling / 6.1: |
Monte Carlo Dynamically Weighted Importance Sampling / 6.3: |
Sequentially Dynamically Weighted Importance Sampling / 6.4: |
Stochastic Approximation Monte Carlo / 7: |
Multicanonical Monte Carlo / 7.1: |
1/k-Ensemble Sampling / 7.2: |
Wang-Landau Algorithm / 7.3: |
Applications of Stochastic Approximation Monte Carlo / 7.4: |
Variants of Stochastic Approximation Monte Carlo / 7.6: |
Theory of Stochastic Approximation Monte Carlo / 7.7: |
Trajectory Averaging: Toward the Optimal Convergence Rate / 7.8: |
Markov Chain Monte Carlo with Adaptive Proposals / 8: |
Stochastic Approximation-based Adaptive Algorithms / 8.1: |
Adaptive Independent Metropolis-Hastings Algorithms / 8.2: |
Regeneration-based Adaptive Algorithms / 8.3: |
Population-based Adaptive Algorithms / 8.4: |
References |
Index |
Acknowledgments |
Publisher's Acknowledgments |
Bayesian Inference and Markov Chain Monte Carlo |
Specification of Bayesian Models / 1.1.1: |
The Jeffreys Priors and Beyond / 1.1.2: |
Bayes Output |
Credible Intervals and Regions / 1.2.1: |
Hypothesis Testing: Bayes Factors / 1.2.2: |
The Problem / 1.3.1: |
Monte Carlo Approximation / 1.3.2: |
Monte Carlo via Importance Sampling / 1.3.3: |
Random Variable Generation |
Direct or Transformation Methods / 1.4.1: |
Acceptance-Rejection Methods / 1.4.2: |
The Ratio-of-Uniforms Method and Beyond / 1.4.3: |
Adaptive Rejection Sampling / 1.4.4: |
Perfect Sampling / 1.4.5: |
Markov Chain Monte Carlo |
Markov Chains / 1.5.1: |
Convergence Results / 1.5.2: |
Convergence Diagnostics / 1.5.3: |
The Gibbs Sampler |
Implementation Strategies and Acceleration Methods |
Blocking and Collapsing / 2.3.1: |
Hierarchical Centering and Reparameterization / 2.3.2: |
Parameter Expansion for Data Augmentation / 2.3.3: |
Alternating Subspace-Spanning Resampling / 2.3.4: |
The Student-t Model / 2.4.1: |
Robit Regression or Binary Regression with the Student-t Link / 2.4.2: |
Linear Regression with Interval-Censored Responses / 2.4.3: |
The EM and PX-EM Algorithms / Appendix 2A: |
Independence Sampler / 3.1.1: |
Random Walk Chains / 3.1.2: |
Problems with Metropolis-Hastings Simulations / 3.1.3: |
Variants of the Metropolis-Hastings Algorithm |
The Hit-and-Run Algorithm / 3.2.1: |
The Langevin Algorithm / 3.2.2: |
The Multiple-Try MH Algorithm / 3.2.3: |
Reversible Jump MCMC Algorithm for Bayesian Model Selection Problems |
Reversible Jump MCMC Algorithm / 3.3.1: |
Change-Point Identification / 3.3.2: |
Metropolis-Within-Gibbs Sampler for ChIP-chip Data Analysis |
Metropolis-Within-Gibbs Sampler / 3.4.1: |
Bayesian Analysis for ChIP-chip Data / 3.4.2: |
The Slice Sampler |
The Møller Algorithm |
The Double MH Sampler |
Spatial Autologistic Models / 4.8.1: |
Monte Carlo MH Algorithm / 4.9.1: |
Convergence / 4.9.2: |
Spatial Autologistic Models (Revisited) / 4.9.3: |
Marginal Inference / 4.9.4: |
Autonormal Models / 4.10.1: |
Social Networks / 4.10.2: |
Evolutionary Monte Carlo in Binary-Coded Space / 5.5.1: |
Evolutionary Monte Carlo in Continuous Space / 5.5.2: |
Implementation Issues / 5.5.3: |
Two Illustrative Examples / 5.5.4: |
Discussion / 5.5.5: |
Sequential Parallel Tempering for Simulation of High Dimensional Systems |
Build-up Ladder Construction / 5.6.1: |
Sequential Parallel Tempering / 5.6.2: |
An Illustrative Example: the Witch's Hat Distribution / 5.6.3: |
Bayesian Curve Fitting / 5.6.4: |
Protein Folding Simulations: 2D HP Model / 5.8.2: |
Bayesian Neural Networks for Nonlinear Time Series Forecasting / 5.8.3: |
Protein Sequences for 2D HP Models / Appendix 5A: |
The IWIW Principle / 6.1.1: |
Tempering Dynamic Weighting Algorithm / 6.1.2: |
Dynamic Weighting in Optimization / 6.1.3: |
The Basic Idea / 6.2.1: |
A Theory of DWIS / 6.2.2: |
Two DWIS Schemes / 6.2.3: |
Weight Behavior Analysis / 6.2.5: |
A Numerical Example / 6.2.6: |
Sampling from Distributions with Intractable Normalizing Constants / 6.3.1: |
Bayesian Analysis for Spatial Autologistic Models / 6.3.2: |
The Wang-Landau Algorithm |
Efficient p-Value Evaluation for Resampling-Based Tests / 7.5.1: |
Bayesian Phylogeny Inference / 7.5.2: |
Bayesian Network Learning / 7.5.3: |
Smoothing SAMC for Model Selection Problems / 7.6.1: |
Continuous SAMC for Marginal Density Estimation / 7.6.2: |
Annealing SAMC for Global Optimization / 7.6.3: |
Convergence Rate / 7.7.1: |
Ergodicity and its IWIW Property / 7.7.3: |
Trajectory Averaging for a SAMCMC Algorithm / 7.8.1: |
Trajectory Averaging for SAMC / 7.8.2: |
Proof of Theorems 7.8.2 and 7.8.3 / 7.8.3: |
Test Functions for Global Optimization / Appendix 7At: |
Stochastic Approximation-Based Adaptive Algorithms |
Ergodicity and Weak Law of Large Numbers / 8.1.1: |
Adaptive Metropolis Algorithms / 8.1.2: |
Regeneration-Based Adaptive Algorithms |
Identification of Regeneration Times / 8.3.1: |
Proposal Adaptation at Regeneration Times / 8.3.2: |
Population-Based Adaptive Algorithms |
ADS, EMC, NKC and More / 8.4.1: |
Adaptive.EMC / 8.4.2: |
Application to Sensor Placement Problems / 8.4.3: |