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Molecular EvolutionA Statistical Approach$
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Ziheng Yang

Print publication date: 2014

Print ISBN-13: 9780199602605

Published to Oxford Scholarship Online: August 2014

DOI: 10.1093/acprof:oso/9780199602605.001.0001

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Bayesian computation (MCMC)

Bayesian computation (MCMC)

Chapter:
(p.214) Chapter 7 Bayesian computation (MCMC)
Source:
Molecular Evolution
Author(s):

Ziheng Yang

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199602605.003.0007

This chapter provides a detailed introduction to modern Bayesian computation. The Metropolis–Hastings algorithm is illustrated using a simple example of distance estimation between two sequences. A number of generic Markov chain Monte Carlo (MCMC) proposal moves are described, and the calculation of their proposal ratios is illustrated. The chapter discusses the convergence rate of the Markov chain as well as its mixing efficiency, as influenced by the MCMC proposal. The chapter also illustrates several advanced MCMC algorithms, including parallel tempering (Metropolis-coupled MCMC or MCMCMC) which uses heated chains to improve mixing when there are multiple local peaks on the posterior surface, reversible jump MCMC (rjMCMC) which is used in trans-model and trans-dimensional inference, and calculation of the Bayes factor used in Bayesian model selection.

Keywords:   Markov chain Monte Carlo, MCMC, Metropolis-coupled Markov chain Monte Carlo, MCMCMC, Metropolis–Hastings, heated chain, parallel tempering, reversible jump, Bayes factor

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