In this work we present a spatial approach to investigate mortality data referenced over a Lexis structure. We decompose the force of mortality into two interpretable components: a Markov random field, homogeneous with respect to age, period and cohort which explains the main pattern of mortality; and a secondary component of independent shocks, accounting for additional non structured patterns. Inference is based on a hierarchical Bayesian model with Markov chain Monte Carlo computations. We present an application to data from the Human Mortality Database, with respect to Italy and Sweden, two countries with very different histories in terms of demographic and epidemiological transitions. For each country the primary surface of spatially structured mortality and the secondary surface of additional mortality are estimated. The importance of each component is evaluated by the estimated value of the respective precision parameter. In both Italy and Sweden, we discovered an interesting band of extra mortality in the secondary surface across the time domain, in the age interval between 60 and 90 years, with a slightly positive slope. The band represents a significant amount of extra mortality for the elderly population, which is otherwise incompatible with a structured dynamics in age, period and cohort.

在这项工作中，我们提出了一种空间方法来调查通过 Lexis 结构引用的死亡率数据。我们将死亡率的力量分解为两个可解释的部分：马尔可夫随机场，在年龄、时期和队列方面是同质的，它解释了死亡率的主要模式；和独立冲击的次要组成部分，解释了额外的非结构化模式。推理基于具有马尔可夫链蒙特卡罗计算的分层贝叶斯模型。我们针对来自人类死亡率数据库的数据提出了一个应用程序，涉及意大利和瑞典，这两个国家在人口和流行病学转变方面有着截然不同的历史。对于每个国家，估计空间结构死亡率的主要表面和额外死亡率的次要表面。每个组件的重要性通过各自精度参数的估计值进行评估。在意大利和瑞典，我们在 60 至 90 岁的年龄区间内，在整个时域的次要表面中发现了一个有趣的额外死亡率带，斜率略为正。该频带代表老年人口的大量额外死亡率，否则这与年龄、时期和队列的结构化动态不相容。