Approximations and consistency of the Bayes factor
as model dimension grows.
J. Berger, J.K Ghosh, and N. Mukhopadhyay
Stone(1979) showed that BIC can fail to be asymptotically consistent.
Note, however, that BIC was developed as an asymptotic approximation
to Bayes factors between models, and that the approximation is valid
only under certain conditions. The counterexample of Stone arises
in situations in which BIC is not an adequate approximation. We
develop some new approximations to Bayes factors, that are valid
for the situation considered in Stone (1979), and discuss related
issues of consistency.