A new method of forecasting mortality is introduced. The method is based on the continuous-time dynamics of the Lexis diagram, which given weak assumptions implies that the death count data are Poisson distributed. The underlying mortality rates are modelled with a hidden Markov model (HMM) which enables a fully likelihood-based inference. Likelihood inference is done by particle filter methods, which avoids approximating assumptions and also suggests natural model validation measures. The proposed model class contains as special cases many previous models with the important difference that the HMM methods make it possible to estimate the model efficiently. Another difference is that the population and latent variable variability can be explicitly modelled and estimated. Numerical examples show that the model performs well and that inefficient estimation methods can severely affect forecasts.

中文翻译：

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使用基于 Lexis 的状态空间模型进行死亡率预测

介绍了一种预测死亡率的新方法。该方法基于 Lexis 图的连续时间动态，给定弱假设意味着死亡人数数据是泊松分布的。潜在死亡率采用隐马尔可夫模型 (HMM) 建模，该模型支持完全基于似然的推理。似然推断是通过粒子过滤方法完成的，它避免了近似假设，并且还提出了自然模型验证措施。所提出的模型类包含许多以前的模型作为特殊情况，其重要区别在于 HMM 方法可以有效地估计模型。另一个区别是总体和潜在变量的可变性可以明确建模和估计。