Semiparametric regression for count data

We introduce a class of Bayesian semiparametric models for regression problems in which the response variable is a count. Our goal is to provide a flexible, easy-to-implement and robust extension of generalised linear models, for datasets of moderate or large size. Our approach is based on modelling the distribution of the response variable using a Dirichlet process, whose mean distribution function is itself random and is given a parametric form, such as a generalised linear model. The effects of the explanatory variables on the response are modelled via both the parameters of the mean distribution function of the Dirichlet process and the total mass parameter. We discuss modelling options and relationships with other approaches. We derive in closed form the marginal posterior distribution of the regression coefficients and discuss its use in inference and computing. We illustrate the benefits of our approach with a prognostic model for early breast cancer patients.