On predictive probability matching priors

Probability Matching Priors

A probability matching prior is a prior distribution under which the posterior probabilities of certain regions coincide with their coverage probabilities, either exactly or approximately. Use of such a prior will ensure exact or approximate frequentist validity of Bayesian credible regions. Probability matching priors have been of interest for many years but there has been a resurgence of inte...

On a Property of Probability Matching Priors: Matching the Alternative Coverage Probabilities

In frequentist inference based on conndence sets, both the true coverage and the probability for a conndence set to include an alternative value of the parameter of interest are important. Thus if probability matching priors also match such alternative coverage probabilities there is perhaps a stronger justiication for calling them noninformative. Considering contiguous alternatives, we obtain ...

On the uniqueness of probability matching priors

Probability matching priors are priors for which Bayesian and frequentist inference, in the form of posterior quantiles, or confidence intervals, agree to some order of approximation. These priors are constructed by solving a first order partial differential equation, that may be difficult to solve. However, Peers (1965) and Tibshirani (1989) showed that under parameter orthogonality a family o...

Constructing second-order data dependent probability matching priors from first-order probability matching priors

On the implementation of local probability matching priors for interest parameters

Probability matching priors are priors for which the posterior probabilities of certain specified sets are exactly or approximately equal to their coverage probabilities. These priors arise as solutions of partial differential equations that may be difficult to solve, either analytically or numerically. Recently Levine & Casella (2003) presented an algorithm for the implementation of probabilit...