Chapter 9

# Markov Chain Monte Carlo Methods

## 9.1 Introduction

Markov Chain Monte Carlo (MCMC) methods encompass a general framework of methods introduced by Metropolis et al. [197] and Hastings [138] for Monte Carlo integration. Recall (see Section 5.2) that Monte Carlo integration estimates the integral

${\int }_{A}g\left(t\right)dt$

with a sample mean, by restating the integration problem as an expectation with respect to some density function f(·). The integration problem then is reduced to finding a way to generate samples from the target density f(·).

The MCMC approach to sampling from f(·) is to construct a Markov chain with stationary distribution f(·), and run the chain for a sufficiently long time until the chain converges (approximately) to its stationary ...

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