There has been growing interest on forecasting mortality. In this article, we propose a novel dynamic Bayesian approach for modelling and forecasting the age-at-death distribution, focusing on a three-component mixture of a Dirac mass, a Gaussian distribution and a skew-normal distribution. According to the specified model, the age-at-death distribution is characterized via seven parameters corresponding to the main aspects of infant, adult and old-age mortality. The proposed approach focuses on coherent modelling of multiple countries, and following a Bayesian approach to inference we allow to borrow information across populations and to shrink parameters towards a common mean level, implicitly penalizing diverging scenarios. Dynamic modelling across years is induced through an hierarchical dynamic prior distribution that allows to characterize the temporal evolution of each mortality component and to forecast the age-at-death distribution. Empirical results on multiple countries indicate that the proposed approach outperforms popular methods for forecasting mortality, providing interpretable insights on its evolution.

中文翻译：

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通过混合偏态分布函数对死亡率进行动态建模

人们对预测死亡率越来越感兴趣。在本文中，我们提出了一种新颖的动态贝叶斯方法来建模和预测死亡年龄分布，重点关注狄拉克质量、高斯分布和偏态正态分布的三分量混合。根据指定的模型，死亡年龄分布通过七个参数来表征，这些参数对应于婴儿、成人和老年死亡率的主要方面。所提出的方法侧重于多个国家的连贯建模，并遵循贝叶斯方法进行推理，我们允许跨人群借用信息并将参数缩小到一个共同的平均水平，隐含地惩罚不同的情景。跨年的动态建模是通过分层动态先验分布诱导的，该分布允许表征每个死亡率成分的时间演变并预测死亡年龄分布。多个国家的经验结果表明，所提出的方法优于预测死亡率的流行方法，为其演变提供了可解释的见解。