Markov–chain Monte Carlo methods for the Box–Behnken designs and centrally symmetric configurations. (2nd January 2016) - Aoki, Satoshi; Hibi, Takayuki; Ohsugi, Hidefumi
ABSTRACT: We consider Markov-chain Monte Carlo methods for calculating conditional p values of statistical models for count data arising in Box–Behnken designs. The statistical model we consider is a discrete version of the first-order model in the response surface methodology. For our models, the Markov basis, a key notion to construct a connected Markov chain on a given sample space, is characterized as generators of the toric ideals for the centrally symmetric configurations of root system Dn . We show the structure of the Gröbner bases for these cases. A numerical example for an imaginary data set is given.