Mathematical foundations of the Markov chain Monte Carlo method (1998)
| Venue: | in Probabilistic Methods for Algorithmic Discrete Mathematics |
| Citations: | 29 - 1 self |
BibTeX
@INPROCEEDINGS{Jerrum98mathematicalfoundations,
author = {Mark Jerrum},
title = {Mathematical foundations of the Markov chain Monte Carlo method},
booktitle = {in Probabilistic Methods for Algorithmic Discrete Mathematics},
year = {1998},
pages = {116--165},
publisher = {Springer-Verlag}
}
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Abstract
7.2 was jointly undertaken with Vivek Gore, and is published here for the first time. I also thank an anonymous referee for carefully reading and providing helpful comments on a draft of this chapter. 1. Introduction The classical Monte Carlo method is an approach to estimating quantities that are hard to compute exactly. The quantity z of interest is expressed as the expectation z = ExpZ of a random variable (r.v.) Z for which some efficient sampling procedure is available. By taking the mean of some sufficiently large set of independent samples of Z, one may obtain an approximation to z. For example, suppose S = \Phi (x; y) 2 [0; 1] 2 : p i (x; y) 0; for all i \Psi<F12
