Bayesian Statistical Modeling: Comparisons Between Poisson and Its Zero-Inflated Regression Model
In this paper, we fit Poisson regression model and its Zero-Inflated version in Bayesian framework, to Malaysian motor vehicle claim count data, in order to study the differences between the models. The models are tested to Third Party Property Damage coverage data which contains sizeable amount of zero claims. The posterior distributions for both models are produced using Markov Chain Monte Carlo (MCMC) simulation to estimate their parameters. The results show that the Bayesian Zero-Inflated Poisson model has superiority over the standard Bayesian Poisson model based on the Deviance Information Criterion (DIC) values.
- 1.Scollnik, D.P.M.: A Bayesian analysis of a simultaneous equations model for insurance rate-making. Insur. Math. Econ. 12(3), 265–286 (1993). https://doi.org/10.1016/0167-6687(93)90238-K
- 2.Denuit, M., Lang, S.: Non-life rate-making with Bayesian GAMs. Insur. Math. Econ. 35(3), 627–647 (2004). https://doi.org/10.1016/j.insmatheco.2004.08.001
- 3.Bermúdez, L., Karlis, D.: Bayesian multivariate Poisson models for insurance ratemaking. Insur. Math. Econ. 48(2), 226–236 (2011). https://doi.org/10.1016/j.insmatheco.2010.11.001
- 5.Pérez-Sánchez, J.M., Gómez-Déniz, E.: Simulating Posterior Distributions for Zero-Inflated Automobile Insurance Data, 47092 (2015)Google Scholar
- 6.Fuzi, M.F.M., Jemain, A.A., Ismail, N.: Bayesian quantile regression model for claim count data. Insur. Math. Econ. 66, 124–137 (2016). https://doi.org/10.1016/j.insmatheco.2015.11.004