A Bayesian Hierarchical Model with Spatial Variable Selection: The Effect of Weather on Insurance Claims

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 geographic scale. The number of weather-related insurance claims is modelled by combining generalized linear models with spatially smoothed variable selection. Using Gibbs sampling and reversible jump Markov chain Monte Carlo methods, this model is fitted on daily weather and insurance data from each of the 319 municipalities which constitute southern and central Norway for the period 1997-2006. Precise out-of-sample predictions validate the model. Our results show interesting regional patterns in the effect 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 for long-term predictions based on downscaled climate models.