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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Markov chain Monte Carlo methods

Markov chain Monte Carlo methods

Chapter:
(p.87) 6 Markov chain Monte Carlo methods
Source:
Bayesian Theory and Applications
Author(s):

Chib Siddhartha

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0006

This chapter provides a brief summary of Markov chain Monte Carlo (MCMC) methods. The chapter is organized as follows. Section 6.2 describes the Metropolis–Hastings algorithm and its generalized version. Section 6.3 considers the Gibbs sampling algorithm while additional topics of importance, such as sampling with latent data and calculation of the marginal likelihood, are discussed in Section 6.4. Section 6.5 has concluding remarks.

Keywords:   MCMC methods, Metropolis–Hastings algorithm, Gibbs sampling algorithm, latent data, marginal likelihood

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