Quantification of observed prior and likelihood information in parametric Bayesian modeling
This work addresses the need for better diagnostic tools in Bayesian modeling, though it appears incremental as it builds on existing information measures like those from Berger, Bernardo, Sun, and Lindley.
The authors tackled the problem of quantifying prior and likelihood information in parametric Bayesian models by developing two data-dependent information metrics, which are shown to be useful diagnostic tools for Bayesian analysis through theoretical, empirical, and computational evidence.
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.