Generalized Empirical Bayes Modeling via Frequentist Goodness of Fit

Abstract

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.

Applied Econometrics

“…This article provides a pragmatic and comprehensive framework for nonlinear time series modeling that is easier to use, more versatile and has a strong theoretical foundation based on the recently-developed theory of unified algorithms of data science via LP modeling (Mukhopadhyay 2016(Mukhopadhyay , 2017Mukhopadhyay and Fletcher 2018;Mukhopadhyay and Parzen 2014;Parzen and Mukhopadhyay 2012. The summary and broader implications of the proposed research are:…”

Breiman's "Two Cultures'' Revisited and Reconciled

“…) and so on. For more information, see Mukhopadhyay and Fletcher (2018), . This will be useful for constructing LP-polynomials for any general pivot density f 0 of the response variable.…”

Exhaustive goodness-of-fit via smoothed inference and graphics

“…LP modeling allows the unification of many of the standard results of classical statistics by expressing them in terms of quantiles and comparison densities (e.g., Mukhopadhyay, 2016;Mukhopadhyay and Fletcher, 2018) and provides a simple and powerful framework for data analysis (e.g., Mukhopadhyay, 2017;Parzen, 2018, 2020;Mukhopadhyay and Wang, 2020). This approach lays its foundations in a specially designed orthonormal basis of LP score functions which, conversely to any other polynomial basis, can be used to express general functions of continuous or discrete random variables and thus provide a universal representation for arbitrary data distributions.…”