Markov bases for two-way change-point models of ladder
determinantal tables
Aoki, Satoshi
Creator
Faculty
aoki@math.kobe-u.ac.jp
Hibi, Takayuki
Creator
MATH / Applied Mathematics
Illinois Institute of Technology
Affiliated department
Conditional test
Contingency table
Distributive lattice
GrÃ¶bner basis
Ideal
Markov basis
Markov chain Monte Carlo
Structural zero
2017
2017-02-08
To evaluate the goodness-of-fit 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, 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 Gr ?obner basis for the distributive lattice. We give a numerical example for actual data.
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