MCMC and GLMs for estimating regression parameters

Mahmoud Elsayed,Amr Soliman

doi:10.1108/jhass-08-2019-0028

Abstract

Purpose The purpose of this study is to estimate the linear regression parameters using two alternative techniques. First technique is to apply the generalized linear model (GLM) and the second technique is the Markov Chain Monte Carlo (MCMC) method. Design/methodology/approach In this paper, the authors adopted the incurred claims of Egyptian non-life insurance market as a dependent variable during a 10-year period. MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate the parameters of interest. However, the authors used the R package to estimate the parameters of the linear regression using the above techniques. Findings These procedures will guide the decision-maker for estimating the reserve and set proper investment strategy. Originality/value In this paper, the authors will estimate the parameters of a linear regression model using MCMC method via R package. Furthermore, MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate parameters to predict future claims. In the same line, these procedures will guide the decision-maker for estimating the reserve and set proper investment strategy.

Highlights

Modeling of random events is one of the most vital research aspects in insurance and actuarial sciences
Markov Chain Monte Carlo (MCMC) uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate the linear regression parameters
MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate parameters to predict future claims

Summary

Introduction

Modeling of random events is one of the most vital research aspects in insurance and actuarial sciences. The aim of this paper is to estimate the linear regression parameters using MCMC and GLM methods for incurred claims of the non-life Egyptian insurance market. Pang et al (2007) emphasized on modeling loss distributions for insurance claims, by considering Pareto distribution to calculate the probability of extreme claims They used Bayesian and MCMC techniques to estimate Pareto parameters. Boj and Costa (2017) estimated the parameters of loss distribution and predicted the error using GLMs to the claim amounts of a chain ladder method. Hogg and Foreman (2018) used MCMC to estimate the density function of the posterior distribution, fitting models to data and probabilistic inferences In this paper, they illustrated the MCMC method and parameter estimation, they concluded that this method provides the best estimate. He concluded that MCMC method is much better than classical methods (e.g. chain ladder and Bayesian over-dispersed Poisson model)

Data and methodology

Markov chain Monte Carlo

Descriptive statistics non-life

Conclusion