Mortality projection incorporating model uncertainty

Jonathan J. Forster, University of Southampton
Xiaoling Ou, University of Southampton

Researchers interested in longevity and mortality projection have available a wide variety of mortality projection models from which to choose. Having been chosen, the favoured model is typically fitted against a suitable dataset and projected forward in time to produce estimated future mortality rates together with an estimate of the associated uncertainty in the form of a prediction interval. However, different models not only yield different best estimates but also generate different prediction intervals. In this paper, we describe a Bayesian statistical approach to the quantification of mortality projection uncertainty that incorporates model uncertainty. Bayesian statistical inference under model uncertainty updates a prior probability distribution over the models to a posterior distribution, in light of observed data. Crucially, this allows predictive probability statements to be made which incorporate model uncertainty. Although the principles of Bayesian inference are straightforward, practical methodology for incorporating probabilistic model uncertainty into mortality forecasts is currently underdeveloped. In this paper, we provide such a methodology. Initially, we focus on individual models, and develop Bayesian methodology for computing the predictive (forecast) distributions for various models. The main contribution of our work is that we demonstrate how to effectively compute probabilistic projections across mortality projection models. We use a computational approach which involves separate Markov chain Monte Carlo (MCMC) generation of parameter values for each model, together with a method which uses the MCMC output to estimate the posterior model probabilities. Our approach is illustrated on data from England and Wales. Using a diverse selection of models, we illustrate how the posterior model probabilities are computed, together with the resulting forecast arising from integrating over the models to account for model uncertainty. The integrated projection uncertainty provides a coherent and more realistic assessment of uncertainty than any corresponding analysis based upon a single model.