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Markov Chain Sampling and the Product Estimator

Author

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  • George S. Fishman

    (University of North Carolina, Chapel Hill, North Carolina)

Abstract

Several recent papers have suggested using a product estimator in Monte Carlo Markov chain sampling for estimating the volume of a convex body, the permanent of a matrix and the distribution of first-passage time for a positive recurrent Markov chain. The present paper analyzes the properties of this estimator when each replication starts in an arbitrarily selected state. In particular, it describes a procedure for determining optimal warm-up intervals and optimal sample sizes to achieve a specified level of statistical accuracy at minimal cost. Also, it examines the variation in the optimal solution in response to changes in the parameters of the problem.

Suggested Citation

  • George S. Fishman, 1994. "Markov Chain Sampling and the Product Estimator," Operations Research, INFORMS, vol. 42(6), pages 1137-1145, December.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:6:p:1137-1145
    DOI: 10.1287/opre.42.6.1137
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    Cited by:

    1. Paredes, R. & Dueñas-Osorio, L. & Meel, K.S. & Vardi, M.Y., 2019. "Principled network reliability approximation: A counting-based approach," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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    Keywords

    simulation: statistical analysis;

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