Some Remarks on Noninformative Priors

Abstract

This article focuses primarily on a comparison between the reference priors of Berger and Bernardo and the reverse reference priors suggested by J. K. Ghosh. Sufficient conditions are given that provide agreement between the two classes of priors. Several examples are given showing the agreement or disagreement between the two. In addition, these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real-valued parametric function to match a nominal level with a remainder of O(n ⁻¹), where n denotes the sample size. The latter priors, first introduced by Welch and Peers, are obtained by solving a differential equation due to Peers. Finally, in the presence of several parameters of interest, a general class of priors that satisfies the matching criterion separately for each parameter is constructed, and examples are given to illustrate how reference or reverse reference priors fit within this class of priors.

Key Words:

• Jeffreys's priors
• Many parameters
• Probability-matching criterion
• Random-effects models
• Reference priors
• Reverse reference priors