Markov Bases for Typical Block Effect Models of Two-way Contingency Tables

TL;DR

This paper derives explicit Markov bases for specific two-way contingency table models, enabling more effective conditional tests via Markov chain Monte Carlo methods, demonstrated with real data.

Contribution

It provides explicit forms of Markov bases for change point and block diagonal effect models, which are new for these types of two-way contingency table models.

Findings

Explicit Markov bases derived for change point models

Markov bases for block diagonal effect models obtained

Conditional tests successfully performed on real data

Abstract

Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via Markov chain Monte Carlo method. In this paper we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are typical block-wise effect models of two-way contingency tables, and perform conditional tests with some real data sets.