Bayesian procedures for testing partial equality of two populations when parameters are exchangeable

Abstract

Bayesian procedures for sharp hypothesis testing have been reviewed in Dickey (1976). These procedures can be adapted to provide a unified approach to testing hypotheses of partial equality of two populations from a parametrized family. It is shown here that the assessment of prior probabilities to be attached to hypersurfaces of different dimensions and, in particular, to the hypotheses of interest can be done in a systematic manner if the parameters are exchangeable. Application to the two multivariate normal populations is suggested.

Keywords:

• exchangeability
• hypersurface
• predictive probabilities
• sharp hypotheses