Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities |
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Authors: | Sooyoung Cheon Faming Liang Yuguo Chen Kai Yu |
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Institution: | 1. Department of Informational Statistics, Korea University, Jochiwon, 339-700, South Korea 2. Department of Statistics, Texas A&M University, College Station, TX, 77843, USA 3. Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, 61820, USA 4. Division of Cancer Epidemiology & Genetics, National Cancer Institute, Rockville, MD, USA
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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. |
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