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

Abstract

To evaluate the goodness-of-t of a statistical model to given data, calculating a conditional p value by a Markov chain Monte Carlo method is one of the eective approaches. For this purpose, a Markov basis plays an important role because it guarantees the connectivity of the chain, which is needed 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, i.e., works on incomplete tables by Aoki and Takemura (2005, J. Stat. Comput. Simulat.) and subtable some constraints by Hara, Takemura and Yoshida (2010, J. Pure Appl. Algebra). Our main result is based on the theory of Grobner basis for the distributive lattice. We give a numerical example for actual data.