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Stopping Tests for Markov Chain Monte-Carlo Methods

Author

Listed:
  • B. Ycart

    (Universite´ Rene´ Descartes
    UFR)

Abstract

Markov Chain Monte-Carlo methods produce a random sample of a given distribution by simulating a Markov chain for which the desired distribution is a reversible measure. In order to generate a sample of size n, we propose to run n independent copies of the chain all starting from the same initial state. If n is large enough, the cutoff phenomenon yields a natural stopping rule. Indeed, the access to equilibrium can be detected using empirical estimates for the expectation of a state function. The method is illustrated by the generation of random samples of stable sets on an undirected graph.

Suggested Citation

  • B. Ycart, 2000. "Stopping Tests for Markov Chain Monte-Carlo Methods," Methodology and Computing in Applied Probability, Springer, vol. 2(1), pages 23-36, April.
    • Handle: RePEc:spr:metcap:v:2:y:2000:i:1:d:10.1023_a:1010003117070
    DOI: 10.1023/A:1010003117070
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    References listed on IDEAS

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    1. William A. Massey, 1987. "Stochastic Orderings for Markov Processes on Partially Ordered Spaces," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 350-367, May.
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    Cited by:

    1. Barrera, Javiera & Lachaud, Béatrice & Ycart, Bernard, 2006. "Cut-off for n-tuples of exponentially converging processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1433-1446, October.

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