CD posterior – combining prior and data through confidence distributions

Abstract

This article proposes an alternative approach to incorporate information from observed data with its corresponding prior information using a recipe developed for combining confidence distributions. The outcome function is called a CD posterior, an alternative to Bayes posterior, which is shown here to have the same coverage property as the Bayes posterior. This approach to incorporating a prior distribution has a great advantage that it does not require any prior on nuisance parameters. It also can ease the computational burden which a typical Bayesian analysis endures. An error bound is established on the CD-posterior when there is an error in prior specification.