Abstract

The holonomic gradient method gives an algorithm to efficiently and accurately evaluate normalizing constants and their derivatives. We apply the holonomic gradient method in the case of the conditional Poisson or multinomial distribution on two-way contingency tables. We utilize the modular method in computer algebra or some other tricks for an efficient and exact evaluation, and we compare them and discuss on their implementation. We also discuss on a theoretical aspect of the distribution from the viewpoint of the conditional maximum likelihood estimation. We decompose parameters of interest and nuisance parameters in terms of sigma algebras for general two-way contingency tables with arbitrary zero cell patterns.

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