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Bayesian ModelsA Statistical Primer for Ecologists$
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N. Thompson Hobbs and Mevin B. Hooten

Print publication date: 2015

Print ISBN-13: 9780691159287

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159287.001.0001

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Markov Chain Monte Carlo

Markov Chain Monte Carlo

Chapter:
(p.145) 7 Markov Chain Monte Carlo
Source:
Bayesian Models
Author(s):

N. Thompson Hobbs

Mevin B. Hooten

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159287.003.0007

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and Smith (1990). It begins with an explanation of MCMC with a heuristic, high-level treatment of the algorithm, describing its operation in simple terms with a minimum of formalism. In this first part, the chapter explains the algorithm so that all readers can gain an intuitive understanding of how to find the posterior distribution by sampling from it. Next, the chapter offers a somewhat more formal treatment of how MCMC is implemented mathematically. Finally, this chapter discusses implementation of Bayesian models via two routes—by using software and by writing one's own algorithm.

Keywords:   Markov chain Monte Carlo, algorithm, MCMC algorithm, posterior distribution, software, Markov chain Monte Carlo

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