Semiparametric Bayesian Count Data Models

Count data models have a large number of pratical applications.
However there can be several problems which prevent the use of the
standard Poisson regression. We may detect individual unobserved
heterogeneity, caused by missing covariates, and/or excess of zero
observations in our data. Both distributional issues results in
deviations of the response distribution from the classical Poisson
assumption. We may in addition want to extend our predictor to
model temporal or spatial correlation and possibly nonlinear
effects of continuous covariates or time scales available in the
data. Here we study and develop semiparametric count data models
which can solve these problems. We have extended the Poisson
distribution to account for overdispersion and/or zero inflation.
Additionally we have incorporated corresponding components in
structured additive form into the predictor. The models are fully
Bayesian and inference is carried out by computationally efficient
MCMC techniques. In simulation studies, we investigate how well the
different components can be identified with the data at hand.
Finally, the approaches are applied to two data sets: to a patent
data set and to a large data set of claim frequencies from car
insurance.