Bayes Factors for Non-Homogeneous Poisson Processes with Vague Prior Information

SUMMARY The calculation of Bayes factors for rival parametric models of non-homogeneous Poisson processes is considered. If vague prior information for the model parameters is represented by limiting improper prior forms, then the resulting Bayes factor is defined only up to a multiplicative constant. It is noted that the procedure proposed by Spiegelhalter and Smith (1982) does not provide any solution to the problem of assigning the constant if the priors are inappropriately specified, and sufficient conditions for it to provide a solution are derived. It is shown that priors which satisfy the conditions exist in most situations. The case of monotonic log-polynomial intensity models is then considered in some detail.