Simulating Posterior Distributions for Zero-Inflated Automobile Insurance Data

TL;DR

This paper introduces a novel Bayesian zero-inflated regression model for automobile insurance data, capable of handling excess zeros and overdispersion, and demonstrates its effectiveness using real Australian insurance data.

Contribution

It develops a flexible Bayesian zero-inflated model based on Power Series Distributions, including special cases like zero-inflated Poisson, with estimation via MCMC in WinBUGS.

Findings

The Bayesian model performs comparably or better than traditional models.

It effectively detects relevant variables affecting insurance premiums.

The approach handles overdispersion and excess zeros in insurance data.

Abstract

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.