Markov Chain Monte Carlo

Stochastic Simulation for Bayesian Inference

Dani Gamerman, Hedibert Lopes - Collection Texts in Stastical Science

344 pages, parution le 10/05/2006 (2^eme édition)

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Résumé

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 adequacy

The 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.

L'auteur - Hedibert Lopes

Hedibert F. Lopes : University of Chicago, Illinois, USA

Sommaire

Stochastic Simulation
- Introduction
- Generation of Discrete Random Quantities
- Generation of Continuous Random Quantities
- Generation of Random Vectors and Matrices
- Resampling Methods
- Exercises
Bayesian Inference
- Introduction
- Bayes' Theorem
- Conjugate Distributions
- Hierarchical Models
- Dynamic Models
- Spatial Models
- Model Comparison
- Exercises
Approximate Methods of Inference
- Introduction
- Asymptotic Approximations
- Approximations by Gaussian Quadrature
- Monte Carlo Integration
- Methods Based on Stochastic Simulation
- Exercises
Markov Chains
- Introduction
- Definition and Transition Probabilities
- Decomposition of the State Space
- Stationary Distributions
- Limiting Theorems
- Reversible Chains
- Continuous State Spaces
- Simulation of a Markov Chain
- Data Augmentation or Substitution Sampling
- Exercises
GIBBS Sampling
- Introduction
- Definition and Properties
- Implementation and Optimization
- Convergence Diagnostics
- Applications
- MCMC-Based Software for Bayesian Modeling
- Appendix 5.A: BUGS Code for Example 5.7
- Appendix 5.B: BUGS Code for Example 5.8
- Exercises
Metropolis-Hastings Algorithms
- Introduction
- Definition and Properties
- Special Cases
- Hybrid Algorithms
- Applications
- Exercises
Further Topics in MCMC
- Introduction
- Model Adequacy
- Model Choice: MCMC Over Model and Parameter Spaces
- Convergence Acceleration
- Exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Dani Gamerman, Hedibert Lopes
Collection	Texts in Stastical Science
Parution	10/05/2006
Édition	2^eme édition
Nb. de pages	344
Format	16 x 24
Couverture	Relié
Poids	610g
Intérieur	Noir et Blanc
EAN13	9781584885870
ISBN13	978-1-58488-587-0