Theory and practice for inference of high dimensional statistical model with computational algebraic geometry.

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In this study we derived Markov bases of some practical models for contingency tables such as homogeneous Markov chain model and split model and proposed practical algorithms of exact tests by using these Markov bases. In general, however, it is not easy to obtain an exact list of a Markov basis for a discrete exponential family model. We gave some practical algorithms of exact test also for such models by using some practical subsets of Markov bases or lattice bases and checked that the performances of proposed algorithms are comparable to the ones by using Markov bases.