Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e., a non-negative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as non-conjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure.
"Variational Inference for Count Response Semiparametric Regression." Bayesian Anal. 10 (4) 991 - 1023, December 2015. https://doi.org/10.1214/14-BA932