DPGLM: A Semiparametric Bayesian GLM with Inhomogeneous Normalized Random Measures

Music City Center 

We introduce a varying weight dependent Dirichlet process (DDP) model to implement a semi-parametric GLM. The model extends a recently developed semi-parametric generalized linear model (SPGLM) by adding a nonparametric Bayesian prior on the baseline distribution of the GLM. We show that the resulting model takes the form of an inhomogeneous normalized random measure that arises from exponential tilting of a normalized completely random measure. Building on familiar posterior simulation methods for mixtures with respect to normalized random measures we introduce posterior simulation in the resulting semi-parametric GLM model. The proposed methodology is validated through a series of simulation studies and is illustrated using data from a speech intelligibility study.

Dependent Dirichlet process

Inhomogeneous normalized random measures

Density regression

Lévy-Khintchine representation

Semiparametric generalized linear model 

Section on Bayesian Statistical Science