Markov basis and Grobner basis of Segre-Veronese configuration for testing independence in group-wise selections

作者：Aoki Satoshi^*; Hibi Takayuki; Ohsugi Hidefumi; Takemura Akimichi

来源：Annals of the Institute of Statistical Mathematics, 2010, 62(2): 299-321.

DOI：10.1007/s10463-008-0171-7

• Contingency table
• Diplotype
• Exact tests
• Haplotype
• Hardy-Weinberg model
• Markov chain Monte Carlo
• National Center Test
• Structural zero

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Grobner basis consisting of binomials of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.

• 出版日期2010-4