#### The Intrinsic Bayes Factor for Linear Models

James O. Berger and Luis R. Pericchi

In Berger and Pericchi (1993) a general automatic Bayesian method for
comparing models, the {\em Intrinsic Bayes Factor\/} (IBF) was
proposed. One version, the {\em Arithmetic IBF\/}, was shown to
essentially correspond to an actual Bayes factor for a reasonable
{\em Intrinsic Prior}. A second version, the {\em Geometric
IBF\/}, is justified in Pericchi and Smith (1993), using a prequential type
of loss function, without assuming that one of the entertained models is
the true sampling model. Here we analyze the general normal linear model,
determining the intrinsic Bayes factors for any model comparisons,
nested or separate, as well as for multiple model comparisons. In these
situations we also calculate the {\em Expected Arithmetic IBF\/}.
We also generalize model elaboration ideas to linear models with
fixed mean structure but arbitrary error distributions. The
method is illustrated on examples and compared with other model
selection methods.
Postscript File (529kB)