Bayesian Modelling of Lexis Mortality Data

Abstract: In this work we present a spatial approach to model and investigate mortality data referenced over a Lexis structure. We decompose the force of mortality into two interpretable components: a Markov random field, smooth with respect to time, age and cohort which explains the main pattern of mortality; and a secondary component of independent shocks, accounting for additional non-smooth mortality. Inference is based on a hierarchical Bayesian approach with Markov chain Monte Carlo computations. We present an extensive application to data from the Human Mortality Database about 37 countries. For each country the primary smooth surface 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. For several countries we discovered a 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 is significant in the most populated countries, but might be present also in the others. The band represents a significant amount of extra mortality for the elderly population, which is otherwise incompatible with a regular and smooth dynamics in age, year and cohort.