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Markov Chain Monte Carlo Stochastic Simulation for Bayesian Inference

ISBN-10: 1584885874
ISBN-13: 9781584885870
Edition: 2nd 2006 (Revised)
List price: $99.95 Buy it from $75.48
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Description: While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds.  More...

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Book details

List price: $99.95
Edition: 2nd
Copyright year: 2006
Publisher: CRC Press LLC
Publication date: 5/10/2006
Binding: Hardcover
Pages: 342
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.342
Language: English

While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration.Major changes from the previous edition: More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection Discussion of computation using both R and WinBUGS Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web Sections on spatial models and model adequacyThe self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.

Preface to the second edition
Preface to the first edition
Introduction
Stochastic simulation
Introduction
Generation of discrete random quantities
Bernoulli distribution
Binomial distribution
Geometric and negative binomial distribution
Poisson distribution
Generation of continuous random quantities
Probability integral transform
Bivariate techniques
Methods based on mixtures
Generation of random vectors and matrices
Multivariate normal distribution
Wishart distribution
Multivariate Student's t distribution
Resampling methods
Rejection method
Weighted resampling method
Adaptive rejection method
Exercises
Bayesian inference
Introduction
Bayes' theorem
Prior, posterior and predictive distributions
Summarizing the information
Conjugate distributions
Conjugate distributions for the exponential family
Conjugacy and regression models
Conditional conjugacy
Hierarchical models
Dynamic models
Sequential inference
Smoothing
Extensions
Spatial models
Model comparison
Exercises
Approximate methods of inference
Introduction
Asymptotic approximations
Normal approximations
Mode calculation
Standard Laplace approximation
Exponential form Laplace approximations
Approximations by Gaussian quadrature
Monte Carlo integration
Methods based on stochastic simulation
Bayes' theorem via the rejection method
Bayes' theorem via weighted resampling
Application to dynamic models
Exercises
Markov chains
Introduction
Definition and transition probabilities
Decomposition of the state space
Stationary distributions
Limiting theorems
Reversible chains
Continuous state spaces
Transition kernels
Stationarity and limiting results
Simulation of a Markov chain
Data augmentation or substitution sampling
Exercises
Gibbs sampling
Introduction
Definition and properties
Implementation and optimization
Forming the sample
Scanning strategies
Using the sample
Reparametrization
Blocking
Sampling from the full conditional distributions
Convergence diagnostics
Rate of convergence
Informal convergence monitors
Convergence prescription
Formal convergence methods
Applications
Hierarchical models
Dynamic models
Spatial models
MCMC-based software for Bayesian modeling
BUGS code for Example 5.7
BUGS code for Example 5.8
Exercises
Metropolis-Hastings algorithms
Introduction
Definition and properties
Special cases
Symmetric chains
Random walk chains
Independence chains
Other forms
Hybrid algorithms
Componentwise transition
Metropolis within Gibbs
Blocking
Reparametrization
Applications
Generalized linear mixed models
Dynamic linear models
Dynamic generalized linear models
Spatial models
Exercises
Further topics in MCMC
Introduction
Model adequacy
Estimates of the predictive likelihood
Uses of the predictive likelihood
Deviance information criterion
Model choice: MCMC over model and parameter spaces
Markov chain for supermodels
Markov chain with jumps
Further issues related to RJMCMC algorithms
Convergence acceleration
Alterations to the chain
Alterations to the equilibrium distribution
Auxiliary variables
Exercises
References
Author index
Subject index

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