Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities
KAUST Grant NumberKUS-C1-016-04
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AbstractImportance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.
CitationCheon S, Liang F, Chen Y, Yu K (2013) Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities. Stat Comput 24: 505–520. Available: http://dx.doi.org/10.1007/s11222-013-9384-6.
SponsorsThe authors thank the editor, associate editor and two referees for their constructive comments which have led to significant improvement of this paper. Cheon's research was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0015000). Liang's research was partially supported by grants from the National Science Foundation (DMS-1007457 and DMS-1106494) and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST). Chen's research was partly supported by the National Science Foundation grant DMS-1106796.
PublisherSpringer Science + Business Media
JournalStatistics and Computing