Multi-output Gaussian processes for multi-population longevity modelling

Abstract

We investigate joint modelling of longevity trends using the spatial statistical framework of Gaussian process (GP) regression. Our analysis is motivated by the Human Mortality Database (HMD) that provides unified raw mortality tables for nearly 40 countries. Yet few stochastic models exist for handling more than two populations at a time. To bridge this gap, we leverage a spatial covariance framework from machine learning that treats populations as distinct levels of a factor covariate, explicitly capturing the cross-population dependence. The proposed multi-output GP models straightforwardly scale up to a dozen populations and moreover intrinsically generate coherent joint longevity scenarios. In our numerous case studies, we investigate predictive gains from aggregating mortality experience across nations and genders, including by borrowing the most recently available “foreign” data. We show that in our approach, information fusion leads to more precise (and statistically more credible) forecasts. We implement our models in R, as well as a Bayesian version in Stan that provides further uncertainty quantification regarding the estimated mortality covariance structure. All examples utilise public HMD datasets.

Joint Models for Cause-of-Death Mortality in Multiple Populations

“…Coregionalization is a dimension reduction technique that enables efficiently handling many correlated outputs. This work is a continuation of our series of articles Ludkovski et al (2018), Huynh et al (2020) and Huynh and Ludkovski (2021) that discussed the application of GPs to model all-cause mortality in the single-population and multi-population contexts, respectively. Unlike all-cause mortality in different geographic regions, which tends to exhibit strong correlation and long-term coherence, different causes have less commonality, and thus require a more flexible structure for the respective cross-dependence.…”

“…As Q is not one of the hyperparameters to be optimized, ad hoc ways are needed to pick it. We use the Bayesian Information Criterion (BIC) to select rank Q that produces the most parsimonious model, see Williams et al (2009) and Huynh and Ludkovski (2021). As discussed in Bonilla et al (2008), taking Q ă L in ICM corresponds to finding a rank-Q approximation (based on an incomplete Cholesky decomposition) to the full-rank C pf q .…”

“…As discussed in Huynh and Ludkovski (2021), MOGPs are well-suited to generate expert-based projections. This is a useful feature to have given that by default projections are driven by the historical trends that might not continue in the future.…”

“…only up to 2014), leading to limited options in terms of the selection and the number of countries we can incorporate with Czech Males in this experiment. Based on our analysis inHuynh and Ludkovski (2021), choosing countries that are highly correlated with Czech Males is essential to maximize the prediction quality.…”

Joint models for cause-of-death mortality in multiple populations

“…As Q is not one of the hyperparameters to be optimised, ad hoc ways are needed to pick it. We use the Bayesian information criterion (BIC) to select rank Q that produces the most parsimonious model; see Williams et al (2009) and Huynh & Ludkovski (2021). As discussed in Bonilla et al (2008), taking Q < L in ICM corresponds to finding a rank-Q approximation (based on an incomplete Cholesky decomposition) to the full-rank C (f ) .…”