Bayesian Modeling via Goodness-of-fit
It addresses fundamental issues in Bayesian statistics for researchers and practitioners, but appears incremental as it builds on existing concepts without claiming major breakthroughs.
The paper tackles the problem of distilling statistical priors consistent with data from initial scientific priors and developing a unified Bayes-frequentist workflow, proposing a 'Bayes via goodness of fit' framework that is general and practical, as shown in illustrative examples.
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 Bayes-frequentist consolidated 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 illustrative examples show the benefit of this new point of view as a practical data analysis tool. Relationship with other Bayesian cultures is also discussed.