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Register a new userMarkov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations
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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 D_n. We show the structure of the Groebner bases for these cases. A numerical example for an imaginary data set is given.
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