Hierarchical Bayesian spatial regression models with applications to non-life insurance
Susanne Gschlößl · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2006
In this thesis the modelling of overdispersed spatial count regression data is addressed. Particular emphasis is given to the Generalized Poisson distribution and zero inflated models. Further, the incorporation of spatial random effects which allows for the modelling of an underlying spatial dependency pattern, forms a central part. For the considered models efficient Markov Chain Monte Carlo (MCMC) algorithms are developed and implemented. In particular a novel Gibbs sampler for spatial Poisson regression models is developed using data augmentation techniques and compared to existing methods. An application to a comprehensive data set from a German car insurance company is given. Spatial regression models for the number of claims and claim size are developed. In contrast to the classical compound Poisson model we allow for dependencies between claim frequency and claim size. Based on these models the total claim sizes are simulated which are fundamental for premium calculation in insurance.