Generalized Empirical Bayes Modeling via Frequentist Goodness of Fit

The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a consolidated Bayes-frequentist data analysis workflow that is more effective than either of the two separately. In this paper, we propose the idea of "Bayes via goodness-of-fit" as a framework for exploring these fundamental questions, in a way that is general enough to embrace almost all of the familiar probability models. Several examples, spanning application areas such as clinical trials, metrology, insurance, medicine, and ecology show the unique benefit of this new point of view as a practical data science tool.