Markov bases for two-way change-point models of ladder determinantal tables

TL;DR

This paper develops Markov bases for two-way change-point models in ladder determinantal tables, extending previous work, and uses Groebner basis theory to ensure connectivity in Markov chain Monte Carlo sampling.

Contribution

It introduces a novel Markov basis construction for the two-way change-point model in ladder determinantal tables using Groebner basis theory.

Findings

Provides a theoretical framework for Markov bases in this setting

Ensures connectivity of Markov chains for unbiased p-value estimation

Includes a numerical example demonstrating the method

Abstract

To evaluate a fitting of a statistical model to given data, calculating a conditional $p$ value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it guarantees the connectivity of the chain for unbiasedness of the estimation, and therefore is investigated in various settings such as incomplete tables or subtable sum constraints. In this paper, we consider the two-way change-point model for the ladder determinantal table, which is an extension of these two previous works. Our main result is based on the theory of Groebner basis for the distributive lattice. We give a numerical example for actual data.