  Generalized linear models (GLMs) using a regression procedure to fit
relationships between predictor and target variables are widely used in
automobile insurance data. Here, in the process of ratemaking and in order to
compute the premiums to be charged to the policy--holders it is crucial to
detect the relevant variables which affect to the value of the premium since in
this case the insurer could eventually fix more precisely the premiums. We
propose here a methodology with a different perspective. Instead of the
exponential family we pay attention to the Power Series Distributions and
develop a Bayesian methodology using sampling--based methods in order to detect
relevant variables in automobile insurance data set. This model, as the GLMs,
allows to incorporate the presence of an excessive number of zero counts and
overdispersion phenomena (variance larger than the mean). Following this
spirit, in this paper we present a novel and flexible zero--inflated Bayesian
regression model. This model includes other familiar models such as the
zero--inflated Poisson and zero--inflated geometric models, as special cases. A
Bayesian estimation method is developed as an alternative to traditionally used
maximum likelihood based methods to analyze such data. For a real data
collected from 2004 to 2005 in an Australian insurance company an example is
provided by using Markov Chain Monte Carlo method which is developed in WinBUGS
package. The results show that the new Bayesian method performs the previous
models.
