Scinovex
articleTop 1% cited

Bayesian Computation Via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods

A. F. M. SmithGareth O. Roberts

Abstract

SUMMARY The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples. Other Markov chain Monte Carlo simulation methods are also briefly described, and comments are made on the advantages of sample-based approaches for Bayesian inference summaries.

Markov Chains and Monte Carlo MethodsBayesian Methods and Mixture ModelsStatistical Methods and Bayesian InferenceMarkov chain Monte CarloGibbs samplingBayesian probabilityComputer scienceParallel temperingMonte Carlo methodApproximate Bayesian computationComputationHybrid Monte CarloStatistical physics
Citations
1,718
FWCI
83.96
field-weighted impact
References
60
Percentile
100%
vs. same field & year
Citations per year
Cited by
Approximate Bayesian Inference with the Weighted Likelihood Bootstrap
Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1994 · 1,509 citations
Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space
Geophysical Journal International · 1999 · 1,503 citations
Geophysical inversion with a neighbourhood algorithm—II. Appraising the ensemble
Geophysical Journal International · 1999 · 813 citations
Estimation of Finite Mixture Distributions Through Bayesian Sampling
Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1994 · 908 citations
Markov Chasin Monte Carlo Algorithms for the Bayesian Analysis of Phylogenetic Trees
Molecular Biology and Evolution · 1999 · 1,618 citations
Assessment and Propagation of Model Uncertainty
Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1995 · 1,583 citations
Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method
Molecular Biology and Evolution · 1997 · 1,313 citations
Bayes Factors
Journal of the American Statistical Association · 1995 · 11,986 citations
References
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence · 1984 · 17,882 citations
Equation of State Calculations by Fast Computing Machines
The Journal of Chemical Physics · 1953 · 36,613 citations
Sampling-Based Approaches to Calculating Marginal Densities
Journal of the American Statistical Association · 1990 · 6,639 citations
Markov Chains for Exploring Posterior Distributions
The Annals of Statistics · 1994 · 3,477 citations
The Calculation of Posterior Distributions by Data Augmentation
Journal of the American Statistical Association · 1987 · 3,753 citations
Citation Network

How this paper connects to the literature. Drag to explore, click any node to open that paper.