A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models

Abstract

Just as frequentist hypothesis tests have been developed to check model assumptions, prior predictive p values and other Bayesian p values check prior distributions as well as the model assumptions that yield the likelihood function. These model checks not only suffer from the usual threshold dependence of p values but also from suppressing model uncertainty in subsequent inference. The proposed solution is to transform Bayesian and frequentist p values for model assessment into a fiducial distribution across the models. Averaging the Bayesian or frequentist posterior distributions with respect to the fiducial distribution in some cases reproduces results from Bayesian model averaging or classical fiducial inference.