Data-dependent probability matching priors for empirical and related likelihoods

TL;DR

This paper explores data-dependent priors for empirical likelihoods to achieve accurate Bayesian credible intervals that align with frequentist confidence levels, especially for empirical likelihood methods.

Contribution

It introduces higher order asymptotic analysis to identify data-dependent priors that ensure probability matching for empirical likelihoods, extending prior work with new positive results.

Findings

Positive results for empirical likelihood with data-dependent priors

Contrast with data-free priors which do not guarantee matching

Higher order asymptotics characterize suitable priors

Abstract

We consider a general class of empirical-type likelihoods and develop higher order asymptotics with a view to characterizing members thereof that allow the existence of possibly data-dependent probability matching priors ensuring approximate frequentist validity of posterior quantiles. In particular, for the usual empirical likelihood, positive results are obtained. This is in contrast with what happens if only data-free priors are entertained.