Bayesian Multiple Comparisons in Geometric Populations

In this paper, we consider the Bayesian multiple comparisons problem for K geometric populations to make inferences on the relationships among parameters based on observations. We introduce the configurations because there is a one to one correspondence between hypotheses and configurations. And we use Bayes factor when noninformative priors are applied for the parameters. But, since noninformative priors are typically improper, the priors are only up to arbitrary constants which affect the values of Bayes factors. Hence, we compute the fractional Bayes factor proposed by O Hagan(1995) to remove the arbitrariness by using a portion of the likelihood with a so-called the fraction b. Also we suggest the Bayesian procedure for multiple comparisons based on fractional Bayes factor by configuration notations. Finally, we give a numerical examples to illustrate our procedure.