DPGLM: A Semiparametric Bayesian GLM with Inhomogeneous Normalized Random Measures

We introduce an extension of a recently developed semi-parametric generalized linear model by adding a nonparametric Bayesian prior on the baseline distribution of the GLM. The construction is similar to a varying-weight dependent Dirichlet process. We show that the resulting model takes the form of an inhomogeneous completely random measure that arises from exponential tilting of a normalized completely random measure. Building on familiar posterior sampling methods for mixtures with respect to normalized random measures, we introduce posterior simulation in the resulting model. We validate the proposed methodology through extensive simulation studies and illustrate its application using data from a speech intelligibility study.