Exact statistical solutions using the inverse Bayes formulae, Pages 305-315

This article extends the inverse Bayes formulae (IBF) in the product measurable space (PMS) to the nonproduct measurable space (NPMS) and focuses on their applications in compatibility checking and Bayesian computation. We show that IBF hold only in PMS and derive the modified IBF in NPMS. The potential of using IBF in obtaining exact solution is demonstrated via problems in distribution theory and several Bayesian missing data models.