A Bayesian hierarchical model with spatial variable selection: the effect of weather on insurance claims. Derivation of distributions and MCMC sampling schemes

Abstract

Climate change will affect the insurance industry. We develop a Bayesian hierarchical statistical approach to explain and predict insurance losses due to weather events at a local geographical scale. The number of weather-related insurance claims is modelled combining generalized linear models with spatially smoothed variable selection. Using Gibbs sampling and reversible jump MCMC, the model is fitted on daily weather and insurance data from each of the 319 municipalities of southern and central Norway for the period 1997-2006. Out-of-sample predictions from the model are very good. Our results show interesting regional patterns in the impact of different weather covariates. In addition to being useful for insurance pricing, our model can be used for short-term predictions based on weather forecasts and long-term predictions based on downscaled climate models.