An Approach to Multi-population Mortality Modeling with Multi-output Gaussian Process Regression

We examine the application of a machine learning method within the spatial statistical framework to simultaneously model multiple longevity surfaces. In particular, we propose the Multi-output Gaussian Process (MOGP) via models of coregionalization as an attractive dimension reduction approach to efficiently scale up to 8~10 populations per fitting. The relationship of co-dependence between populations can be inferred from the cross-correlation matrix. Formulated under the Bayesian paradigm, MOGP enjoys a rich uncertainty quantification and generates full stochastic trajectories for out-of-sample forecasts. We demonstrate the model feature to achieve the coherent long-term forecasts while capturing the commonality in the mortality experience. Through numerous case studies, we illustrate the opportunity of data fusion in joint models to mitigate the model risk, thus boosting the forecast credibility over single-output models. Our framework can handle datasets with varied historical data coverage, an important advantage to possess  better ‘present-date’ mortality forecasts for a domestic population. All the illustrations rely on all-cause mortality datasets from the Human Mortality Database and cause-specific mortality datasets from the Cause-of-death Mortality Database.