A METHOD FOR TESTING NESTED POINT NULL HYPOTHESES USING MULTIPLE BAYES FACTOR

HEA-JUNG KIM

Department of Statistics, Dongguk University, Seoul 100-715, Korea

(Received January 17, 1997; revised February 27, 1998)

Abstract. As a flexible Bayesian test criterion for nested point null hypotheses, asymmetric and multiple Bayes factors are introduced in the form of a modified Savage-Dickey density ratio. This leads to a simple method for obtaining pairwise comparisons of hypotheses in a statistical experiment with a partition on the parameter space. The method is derived from the fact that in general, the asymmetric Bayes factor can be written as the product of the Savage-Dickey ratio and a correction factor where both terms are easily estimated by means of posterior simulation. Analyses of a censored data problem and a serial correlation problem are illustrated for the method. For these cases, the method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required tests.

Key words and phrases: Asymmetric and multiple Bayes factors, Savage-Dickey density ratio, Gibbs sampler, point null hypothesis, censored data, serial correlation.