On the use of stochastic approximation Monte Carlo for Monte Carlo integration
KAUST Grant NumberKUS-C1-016-04
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AbstractThe 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. © 2008 Elsevier B.V. All rights reserved.
CitationLiang F (2009) On the use of stochastic approximation Monte Carlo for Monte Carlo integration. Statistics & Probability Letters 79: 581–587. Available: http://dx.doi.org/10.1016/j.spl.2008.10.007.
SponsorsThe author's research was supported in part by the grant (DMS-0607755) made by the National Science Foundation and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST). The author thanks Professors Chuanhai Liu and Minghui Chen for their early discussions on the topic, and thanks Professor Hira Koul, the associate editor, and the referee for their comments which have led to significant improvement of this paper.
JournalStatistics & Probability Letters