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We consider Markov chain Monte Carlo methods for calculating conditional pvalues of statistical models for count data arising in Box-Behnken designs. Thestatistical model we consider is a discrete version of the first-order model inthe response surface methodology. For our models, the Markov basis, a keynotion to construct a connected Markov chain on a given sample space, ischaracterized as generators of the toric ideals for the centrally symmetricconfigurations of root system D_n. We show the structure of the Groebner basesfor these cases. A numerical example for an imaginary data set is given.

Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations