Alternative priors for a contaminated exponential model evaluated in an insurance loss context

Abstract

This paper builds on the Bayesian framework for inference in the contaminated exponential model, with particular emphasis on the role of prior assumptions regarding the proportion of outliers. While a beta prior is standard in this context, we investigate alternative prior choices that offer greater flexibility in modelling atypical observations. Through simulation studies that span a wide range of parameter configurations, we demonstrate that these alternative priors can yield more insightful inference, particularly in small-sample settings where Bayesian methods are known to offer clear advantages. The practical relevance of the proposed approach is illustrated using a large insurance loss dataset and a smaller random subsample thereof. In both cases, the methodology enables identification of potential outliers by integrating full conditional posterior probabilities, which combine both data-driven evidence and prior assumptions. This unified perspective contrasts with the frequentist approach, where outlier detection depends solely on the observed data. To assess the sensitivity of inference to prior selection, we utilise the Wasserstein Impact Measure, which offers a clear measurement of the effect of prior specifications on posterior conclusions. Overall, the framework enhances both the theoretical understanding and practical implementation of outlier detection in contaminated exponential models, offering a valuable contribution to actuarial science and applied statistical modelling.