Faming Liang, Chuanhai Liu, Raymond Carroll

Advanced Markov Chain Monte Carlo Methods (eBook, PDF)

Learning from Past Samples

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 384
• Erscheinungstermin: 9. Juni 2010
• Englisch
• ISBN-13: 9780470669730
• Artikelnr.: 37298646

Autorenporträt

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.

Inhaltsangabe

Preface. 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 Build-up Ladder Construction. 5.6.2 Sequential Parallel
Tempering. 5.6.3 An Illustrative Example: the Witch's Hat Distribution.
5.6.4 Discussion. 5.7 Equi-Energy Sampler. 5.8 Applications. 5.8.1 Bayesian
Curve Fitting. 5.8.2 Protein Folding Simulations: 2D HPModel. 5.8.3
Bayesian Neural Networks for Nonlinear Time Series Forecasting. Exercises.
Appendix 5A: Protein Sequences for 2D HPModels. 6 Dynamic Weighting. 6.1
DynamicWeighting. 6.1.1 The IWIWPrinciple. 6.1.2 Tempering DynamicWeighting
Algorithm. 6.1.3 DynamicWeighting in Optimization. 6.2 DynamicallyWeighted
Importance Sampling. 6.2.1 The Basic Idea. 6.2.2 A Theory of DWIS. 6.2.3
Some IWIWp Transition Rules. 6.2.4 Two DWIS Schemes. 6.2.5 Weight Behavior
Analysis. 6.2.6 A Numerical Example. 6.3 Monte Carlo Dynamically Weighted
Importance Sampling. 6.3.1 Sampling from Distributions with Intractable
Normalizing Constants. 6.3.2 Monte Carlo Dynamically Weighted Importance
Sampling. 6.3.3 Bayesian Analysis for Spatial Autologistic Models. 6.4
Sequentially Dynamically Weighted Importance Sampling. Exercises. 7
Stochastic Approximation Monte Carlo. 7.1 MulticanonicalMonte Carlo. 7.2
1/k-Ensemble Sampling. 7.3 TheWang-Landau Algorithm. 7.4 Stochastic
ApproximationMonte Carlo. 7.5 Applications of Stochastic ApproximationMonte
Carlo. 7.5.1 Efficient p-Value Evaluation for Resampling-Based Tests. 7.5.2
Bayesian Phylogeny Inference. 7.5.3 Bayesian Network Learning. 7.6 Variants
of Stochastic ApproximationMonte Carlo. 7.6.1 Smoothing SAMC forModel
Selection Problems. 7.6.2 Continuous SAMC for Marginal Density Estimation.
7.6.3 Annealing SAMC for Global Optimization. 7.7 Theory of Stochastic
ApproximationMonte Carlo. 7.7.1 Convergence. 7.7.2 Convergence Rate. 7.7.3
Ergodicity and its IWIWProperty. 7.8 Trajectory Averaging: Toward the
Optimal Convergence Rate. 7.8.1 Trajectory Averaging for a SAMCMC
Algorithm. 7.8.2 Trajectory Averaging for SAMC. 7.8.3 Proof of Theorems
7.8.2 and 7.8.3. Exercises. Appendix 7A: Test Functions for Global
Optimization. 8 Markov Chain Monte Carlo with Adaptive Proposals. 8.1
Stochastic Approximation-Based Adaptive Algorithms. 8.1.1 Ergodicity
andWeak Law of Large Numbers. 8.1.2 AdaptiveMetropolis Algorithms. 8.2
Adaptive IndependentMetropolis-Hastings Algorithms. 8.3 Regeneration-Based
Adaptive Algorithms. 8.3.1 Identification of Regeneration Times. 8.3.2
Proposal Adaptation at Regeneration Times. 8.4 Population-Based Adaptive
Algorithms. 8.4.1 ADS, EMC, NKC andMore. 8.4.2 Adaptive EMC. 8.4.3
Application to Sensor Placement Problems. Exercises. References. Index.