In this paper we propose a method for estimating the parameters of the aging process in order to construct mortality tables when the data is a discrete time sample of the chronological age, while no direct observations of the aging process are available. Here, the aging process is modelled through a Markov jump process with finite state space and a single absorbing state. The non-absorbing states represent the physiological ages and the absorbing state the death, so the time until death follows a phase-type distribution. A Bayesian approach has been considered, specifically a Gibbs sampler method, as part of the algorithm, we use an alternative of the uniformization method applied to Markov bridges. A simulation-based analysis has been carried out to validate the approach. Moreover, the proposed estimation algorithm has been applied to analyze two types of records of mortality real data and to construct the corresponding mortality tables, which are compared with the observed mortality.

中文翻译：

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通过老化过程对死亡率模型进行贝叶斯估计

在本文中，我们提出了一种估计老化过程参数的方法，以便在数据是实足年龄的离散时间样本时构建死亡率表，而没有对老化过程的直接观察。在这里，老化过程通过具有有限状态空间和单一吸收状态的马尔可夫跳跃过程建模。非吸收状态代表生理年龄，吸收状态代表死亡，因此死亡时间服从相型分布。已经考虑了贝叶斯方法，特别是 Gibbs 采样器方法，作为算法的一部分，我们使用适用于马尔可夫桥的均匀化方法的替代方法。已经进行了基于仿真的分析以验证该方法。而且，