Reference priors for constrained rate models of count data

We derive reference priors for constrained rate models of count data using the sequential algorithm of Berger and Bernardo (1992b). The event counts for various groups of subjects are modeled as discrete random variables (Poisson, binomial, or negative binomial) with group specific rates. We consider situations in which the groups can be completely ordered according to one covariate. The priors enforce monotonicity (or monotonicity and convexity) of the rates with respect to the ordering. We use the priors to model a data set on mortality rates for men in different age groups assuming that the mortality rates increase with respect to age. We also consider the situation in which the parameter space is augmented to include rates corresponding to unobserved age groups, and the case of a random upper bound on the mortality rates. In addition, we provide an evaluation of the out-of-sample predictive performance of the proposed methods.