title: A Kullback-Leibler Divergence for Bayesian Model Diagnostics.
abstract: This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert [1] when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike [2]). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also examine the impact of this asymptotic property when the regularity conditions are partially satisfied. Furthermore, the connection between the Goutis-Robert-Akaike KLD and a weighted posterior predictive p-value (WPPP) is established. Finally, both the Goutis-Robert-Akaike KLD and WPPP are applied to compare models using various simulated examples as well as two cohort studies of diabetes.
authors.affiliation: Department of Epidemiology and Biostatistics, University of Texas Health Science Center, San Antonio, USA.
authors.forename: Chen-Pin
authors.initials: CP
authors.lastname: Wang
authors.affiliation: Department of Statistics, University of Florida, Gainesville, USA.
authors.forename: Malay
authors.initials: M
authors.lastname: Ghosh
keywords: Kullback-Leibler Distance; Model Diagnostic; Weighted Posterior Predictive p-Value