A Unified Bayesian Framework for Mortality Model Selection

Abstract: In recent years, a wide range of mortality models has been proposed to address the diverse factors influencing mortality rates, which has highlighted the need to perform model selection. Traditional mortality model selection methods, such as AIC and BIC, often require fitting multiple models independently and ranking them based on these criteria. This process can fail to account for uncertainties in model selection, which can lead to overly optimistic prediction interval, and it disregards the potential insights from combining models. To address these limitations, we propose a novel Bayesian model selection framework that integrates model selection and parameter estimation into the same process. This requires creating a model building framework that will give rise to different models by choosing different parametric forms for each term. Inference is performed using the reversible jump Markov chain Monte Carlo algorithm, which is devised to allow for transition between models of different dimensions, as is the case for the models considered here. We develop modelling frameworks for data stratified by age and period and for data stratified by age, period and product. Our results are presented in two case studies.