Markov–chain Monte Carlo methods for the Box–Behnken designs and centrally symmetric configurations. (2nd January 2016)

• Record Type: Journal Article
• Authors: Aoki, Satoshi; Hibi, Takayuki; Ohsugi, Hidefumi
• Is Part Of: Journal of statistical theory and practice. Volume 10:Number 1(2016)
• Page Start: 59
• Page End: 72
• Publication Date: 2016-01-02
• Subjects: Box-Behnken designs -- centrally symmetric configurations -- Markov bases -- Markov-chain Monte Carlo methods -- root systems; 62K15 -- 62D05 -- 13P10; 519.505
• DOI: 10.1080/15598608.2015.1067172
• Languages: English
• ISSNs: 1559-8608

Abstract

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.