David R. Bickel, University of Ottawa, Canada

The entropy-maximizing Bayesian model of sufficiently small codelength

Inference has to proceed in some way even after a Bayesian model is found to be inadequate, perhaps due to excessive codelength. Should the researcher infer that no conclusions can be drawn? If not, what conclusion may be drawn and with what posterior probability does the conclusion hold? To address this issue, a two-stage procedure is proposed. The first stage checks each model within a large class of models to assess which models have sufficiently small codelength for purposes of data analysis. The resulting set of small-codelength models is then used in the second stage either for summarizing a combined posterior such as a maximum-entropy posterior or for inference according to decision rules of the robust Bayes approach and of imprecise probability more generally.