Computing p-values in conditional independence models for a contingency table

摘要

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. Keywords Markov basis - Markov property - Sparse contingency table - Markov chain Monte Carlo This research is supported by the Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C), No 20500263.