Quantifying the Information of the Prior and Likelihood in Parametric Bayesian Modeling
I suggest using a pair of metrics 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 of Berger and Bernardo (Bernardo 1979, Berger and Bernardo 2009) and information measure introduced by Lindley (Lindley 1956). A Monte Carlo algorithm to estimate these metrics is developed and their properties are explored via a combination of theoretical results, simulations, and applications to public medical data sets. This combination of theoretical, empirical, and computational support provides evidence that these metrics may be useful diagnostic tools when performing a Bayesian analysis.