  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.
