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.

中文翻译：

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多人口寿命建模的多输出高斯过程

我们使用高斯过程 (GP) 回归的空间统计框架研究长寿趋势的联合建模。我们的分析受到人类死亡率数据库 (HMD) 的推动，该数据库为近 40 个国家提供统一的原始死亡率表。然而，很少有随机模型可以同时处理两个以上的群体。为了弥合这一差距，我们利用机器学习中的空间协方差框架，将群体视为因子协变量的不同水平，明确捕捉跨群体的依赖性。所提出的多输出 GP 模型可以直接扩展到十几个人口，而且本质上会产生连贯的联合寿命情景。在我们众多的案例研究中，我们调查了汇总不同国家和性别的死亡率经验的预测收益，包括借用最近可用的“外国”数据。我们表明，在我们的方法中，信息融合会导致更精确（并且在统计上更可信）的预测。我们在R，以及贝叶斯版本斯坦这为估计的死亡率协方差结构提供了进一步的不确定性量化。所有示例都使用公共 HMD 数据集。