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Computing p-values in conditional independence models for a contingency table |
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| Authors: | Masahiro Kuroda Hiroki Hashiguchi Shigakazu Nakagawa |
| Affiliation: | 1. Department of Socio-Information, Okayama University of Science, 1-1 Ridaicho, Okayama, 700-0005, Japan 2. Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama, 338-8570, Japan 3. Department of Computer Science and Mathematics, Kurashiki University of Science and the Arts, 2640 Nishinoura, Tsurajima-cho, Kurashiki-shi, Okayama, 712-8505, Japan |
| Abstract: | We present a Markov chain Monte Carlo (MCMC) method for generating Markov chains using Markov bases for conditional independence models for a four-way contingency table. We then describe a Markov basis characterized by Markov properties associated with a given conditional independence model and show how to use the Markov basis to generate random tables of a Markov chain. The estimates of exact p-values can be obtained from random tables generated by the MCMC method. Numerical experiments examine the performance of the proposed MCMC method in comparison with the χ 2 approximation using large sparse contingency tables. |
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