Introduction to Monte Carlo Methods
This chapter describes a sequence of Monte Carlo methods: importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling. For each method, we discuss whether the method is expected to be useful for high—dimensional problems such as arise in inference with graphical models. After the methods have been described, the terminology of Markov chain Monte Carlo methods is presented. The chapter concludes with a discussion of advanced methods, including methods for reducing random walk behaviour.
For details of Monte Carlo methods, theorems and proofs and a full list of references, the reader is directed to Neal (1993), Gilks, Richardson and Spiegelhalter (1996), and Tanner (1996).
KeywordsMarkov Chain Monte Carlo Method Ising Model Gibbs Sampling Importance Sampling
Unable to display preview. Download preview PDF.
- Neal, R. M.: 1993, Probabilistic inference using Markov chain Monte Carlo methods, Technical Report CRG-TR-93–1, Dept. of Computer Science, University of Toronto.Google Scholar
- Neal, R. M.: 1995, Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation, Technical Report 9508, Dept. of Statistics, University of Toronto.Google Scholar
- Neal, R. M.: 1996, Bayesian Learning for Neural Networks, number 118 in Lecture Notes in Statistics, Springer, New York.Google Scholar
- Thomas, A., Spiegelhalter, D. J. and Gilks, W. R.: 1992, BUGS: A program to perform Bayesian inference using Gibbs sampling, inJ. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds), Bayesian Statistics 4, Clarendon Press, Oxford, pp. 837–842.Google Scholar
- Yeomans, J.: 1992, Statistical mechanics of phase transitions, Clarendon Press, Oxford.Google Scholar