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Biometrika 1973 60(3):607-612; doi:10.1093/biomet/60.3.607
© 1973 by Biometrika Trust
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Optimum Monte-Carlo sampling using Markov chains

P. H. PESKUN

York University Toronto

The sampling method proposed by Metropolis et al. (1953) requires the simulation of a Markov chain with a specified {pi} as its stationary distribution. Hastings (1970) outlined a general procedure for constructing and simulating such a Markov chain. The matrix P of transition probabilities is constructed using a defined symmetric function sij and an arbitrary transition matrix Q. Here, for a given Q, the relative merits of the two simple choices for sij suggested by Hastings (1970) are discussed. The optimum choice for sij is shown to be one of these. For the other choice, those Q are given which are known to make the sampling method based on P asymptotically less precise than independent sampling.

Key Words: Monte-Carlo estimation • Markov chain method of sampling • Variance reduction • Simulation


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