Bayesian Hierarchical Risk Premium Modeling with Model Risk: Addressing Non-Differential Berkson Error

For general insurance pricing, aligning losses with accurate premiums is crucial for insurance companies’ competitiveness. Traditional actuarial models often face challenges like data heterogeneity and mismeasured covariates, leading to misspecification bias. This paper addresses these issues from a Bayesian perspective, exploring connections between Bayesian hierarchical modeling, partial pooling techniques, and the Gustafson correction method for mismeasured covariates. We focus on Non-Differential Berkson (NDB) mismeasurement and propose an approach that corrects such errors without relying on gold standard data. We discover the unique prior knowledge regarding the variance of the NDB errors, and utilize it to adjust the biased parameter estimates built upon the NDB covariate. Using simulated datasets developed with varying error rate scenarios, we demonstrate the superiority of Bayesian methods in correcting parameter estimates. However, our modeling process highlights the challenge in accurately identifying the variance of NDB errors. This emphasizes the need for a thorough sensitivity analysis of the relationship between our prior knowledge of NDB error variance and varying error rate scenarios.