Title: An alternative to objective Bayes model selection
Authors: Monica Musio - University of Cagliari (Italy) [presenting]
Philip Dawid - University of Cambridge (United Kingdom)
Abstract: The use of ``objective'' improper prior distributions for Bayesian model selection is problematic, on account of the non-existence of a finite normalising constant. This leads to an undefined Bayes factor. There have been numerous attempts to circumvent this problem, all involving greater or lesser departure from coherent Bayesian principles. An alternative approach is presented, based on replacing the log score in the definition of the Bayes factor by a local proper scoring rule, such as that of Hyvarinen, which will not involve the normalising constant. The resulting model selection procedure, when conducted prequentially, will be consistent under mild conditions. The theory is illustrated by a number of examples.