Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

Sooyoung Cheon, Faming Liang, Yuguo Chen, Kai Yu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Importance 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.
Original languageEnglish (US)
Pages (from-to)505-520
Number of pages16
JournalStatistics and Computing
Volume24
Issue number4
DOIs
StatePublished - Feb 16 2013
Externally publishedYes

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