Modelagem de prêmios de seguros de automóveis via Aproximação de Laplace Aninhada Integrada (INLA)

Abstract

In this dissettation we carried out Bayesian analysis for auto insurance data using latent Gaussian models. Such class of models include generalized linear (mixed) models and can take various structures, such as temporal, spatial and spatiotemporal. To evaluate the marginal posterior distributions we use the Integrated Nested Laplace Approximation (INLA). This is a fast deterministic algorithm for Bayesian inference with direct application to latent Gaussian models. Model selection was based on Deviance Information Criterion (DIC) as well as the log pseudo marginal likelihood (LPML) that measures the predictive quality of the model and is based on the conditional predictive density ordinate (CPO). To check the model calibration, a histogram of probability integral transform (PIT) was drawn in which we verify the uniformity of the data. In view of the results to drivers premium, we conclude that males pay a higher premium than females, on average. Similarly, youngers pay on average a higher premium than more experienced drivers. We also emphasize that the model that best adjust to data, includes grouping (random) effects, and those are best modelled including spatial effects. Keywords: Automobile Insurance, Gamma Distribution, Gaussian Latent Models, Spatial Models.