DIC in variable selection

Model comparison is discussed from an information theoretic point of view. In particular the posterior predictive entropy is related to the target yielding DIC and modifications thereof. The adequacy of criteria for posterior predictive model comparison is also investigated depending on the comparison to be made. In particular variable selection as a special problem of model choice is formalized in different ways according to whether the comparison is a comparison across models or within an encompassing model and whether a joint or conditional sampling scheme is applied. DIC has been devised for comparisons across models. Its use in variable selection and that of other criteria is illustrated for a simulated data set.