Quantification of observed prior and likelihood information in parametric Bayesian modeling

TL;DR

This paper introduces two data-dependent information metrics for Bayesian models that quantify prior and likelihood information, supported by theoretical, empirical, and computational evidence to serve as diagnostic tools.

Contribution

It develops novel information metrics related to reference priors and Lindley's measure, offering new diagnostic tools for Bayesian analysis.

Findings

Metrics effectively quantify prior and likelihood information.

Metrics align with established reference priors and Lindley's measure.

Support from theoretical, empirical, and computational analyses.

Abstract

Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and Sun, and information measure introduced by Lindley. A combination of theoretical, empirical, and computational support provides evidence that these information-theoretic metrics may be useful diagnostic tools when performing a Bayesian analysis.