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Markov-chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations. (English) Zbl 1420.62334

Summary: 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 Gröbner bases for these cases. A numerical example for an imaginary data set is given.

MSC:

62K15 Factorial statistical designs
62D05 Sampling theory, sample surveys
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)

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References:

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