Markov Chain Monte Carlo

MCMC provides a method for estimating expectations like

$\int d{\bf x}\, f({\bf x})\pi({\bf x})$

in situations where standard analytic or simulation methods are unavailable or inconvenient. This is almost always the cases for Bayesian modeling.

The basic idea is to construct a Markov chain that is is easy to simulate and has $\pi({\bf x})$ as its equilibrium distribution. Then, if ${\bf X}_1, {\bf X}_2, \ldots, {\bf X}_N$ is a realization from such a chain, we have

${1\over N}\sum_{i=1}^N f(X_i) \rightarrow E_\pi[f(X)]$

Note that successive $X_i$ are not uncorrelated.

Send suggestions, questions, and feedback to WEINBERG at ASTRO dot UMASS dot EDU.
Documentation generated at Fri Mar 26 00:35:11 2010 by

BIE

Markov Chain Monte Carlo