Theoretical Application Analysis of Bayesian Inference in Time Series Forecasting of Mortality

Abstract

Population mortality rate prediction is a key issue in pension pricing and insurance product design and a fundamental problem in demography and actuarial science. The Lee-Carter model has been shown to fit well in the long run, however, the frequentist framework is not well adapted to fully account for parameter uncertainty and does not offer a natural way to incorporate prior information. The bias of estimation is particularly problematic when the sample size is small. Bayesian inference takes the prior distribution and the likelihood function and produces the posterior distribution, which is a full probabilistic statement of mortality rate prediction. This work presents a theoretical review on the internal logic and technological pathways of the Bayesian Lee-Carter model, hierarchical models and model averaging methods. It is observed that the advantages of Bayesian approaches are in combining many sources of data, measuring uncertainty and sparse data, especially ideal for long-term prediction scenarios. However, they still have substantial limitations in reliably recovering age-specific mortality statistics, in constructing suitable prior distributions, and in computational efficiency. The real methodological contribution of Bayesian inference is to encourage the move from point estimation to probability prediction in the mortality rate prediction. This change is of considerable practical importance for actuarial practice and for policy analysis.