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A Kullback-Leibler Divergence for Bayesian Model Diagnostics

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DOI: 10.4236/ojs.2011.13021    4,171 Downloads   7,411 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

C. Wang and M. Ghosh, "A Kullback-Leibler Divergence for Bayesian Model Diagnostics," Open Journal of Statistics, Vol. 1 No. 3, 2011, pp. 172-184. doi: 10.4236/ojs.2011.13021.

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