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On the use of stochastic approximation Monte Carlo for Monte Carlo integration

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  • Liang, Faming

Abstract

The stochastic approximation Monte Carlo (SAMC) algorithm has recently been proposed as a dynamic optimization algorithm in the literature. In this paper, we show in theory that the samples generated by SAMC can be used for Monte Carlo integration via a dynamically weighted estimator by calling some results from the literature of nonhomogeneous Markov chains. Our numerical results indicate that SAMC can yield significant savings over conventional Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, for the problems for which the energy landscape is rugged.

Suggested Citation

  • Liang, Faming, 2009. "On the use of stochastic approximation Monte Carlo for Monte Carlo integration," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 581-587, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:581-587
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Liang, Faming & Liu, Chuanhai & Carroll, Raymond J., 2007. "Stochastic Approximation in Monte Carlo Computation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 305-320, March.
    3. Liang F. & Wong W.H., 2001. "Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 653-666, June.
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    Cited by:

    1. Faming Liang & Momiao Xiong, 2013. "Bayesian Detection of Causal Rare Variants under Posterior Consistency," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-16, July.
    2. Cao, Jiajia & Zhou, Yanbin & Wei, Kun, 2024. "Modeling ants’ walks in patrolling multiple resources using stochastic approximation partial momentum refreshment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).

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