Bayesian estimation for a mortality model via the aging process

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.

Keywords

mortality model, physiological age, phase-type distributions, Gibbs sampler, uniformization

2010 Mathematics Subject Classification

Primary 62P05. Secondary 62C10.

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Luz Judith R. Esparza would like to acknowledge the support from CONACYT Mexico. Baltazar-Larios has been supported by UNAM-DGAPA-PAPIIT, Mexico (Project IA105716).

Received 30 August 2020

Accepted 20 March 2021

Published 11 August 2021