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

Satoshi Aoki, Takayuki Hibi

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.


Keywords


Conditional test, Contingency table, Distributive lattice, Gr ̈obner basis, Ideal, Markov basis, Markov chain Monte Carlo, Structural zero.

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DOI: http://dx.doi.org/10.18409/jas.v8i1.55

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