Holonomic Gradient Method for Two Way Contingency Tables

TL;DR

This paper introduces an efficient holonomic gradient method for evaluating normalizing constants in two-way contingency tables, combining algebraic and statistical techniques for improved accuracy and computational complexity.

Contribution

It applies the holonomic gradient method to two-way contingency tables, integrating computer algebra for exact evaluation and analyzing the distribution from a maximum likelihood perspective.

Findings

Efficient evaluation of normalizing constants using the holonomic gradient method.

Implementation of the modular method for exact computations.

Analysis of the distribution's properties via conditional maximum likelihood.

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 for an efficient and exact evaluation, and we discuss on complexities of these algorithms and their implementation. We also discuss on a theoretical aspect of the distribution from the viewpoint of the conditional maximum likelihood estimation.