Title: A Note on Bayesian Model Selection for Discrete Data Using Proper Scoring Rules,
Abstract: We consider the problem of choosing between parametric models for a discrete
observable, taking a Bayesian approach in which the within-model prior
distributions are allowed to be improper. In order to avoid the ambiguity in
the marginal likelihood function in such a case, we apply a homogeneous scoring
rule. For the particular case of distinguishing between Poisson and Negative
Binomial models, we conduct simulations that indicate that, applied
prequentially, the method will consistently select the true model.