Comment on article by Celeux et al.

Abstract

This discussion argues that any difficulty with DIC for missing data is due to DIC being intrinsically a large-sample measure and relying on point estimates. What is missing is not "missing data", but rather a set of coherent principles for DIC itself when the amount of data is not adequate to invoke quadratic approximation for a complex model. The non-uniqueness of data augmentation schemes for any observed-data model also argues for the importance of emphasizing inference "focus" in applying model complexity measures such as DIC. An attempt to bring in more Bayesian "flavor" into DIC also reveals that an insightful explanation is missing: neither pure Bayesian measure nor pure likelihood/sampling measure yield sensible results, but some hybrid ones do.