Summarising mortality data with a time-dependent beta latent variable model

TL;DR

This paper introduces a Bayesian time-dependent beta latent variable model to effectively summarize and reconstruct complex mortality data across countries and ages, outperforming traditional methods.

Contribution

The paper develops a novel time-dependent BLV model with autoregressive priors, enabling better summarization and interpretation of mortality data without data transformation.

Findings

The model accurately reconstructs observed mortality data.

Time-dependent BLV outperforms Gaussian factor analysis.

Parameters provide intuitive and insightful interpretations.

Abstract

Age-specific probabilities of death provide a snapshot of population mortality at the country level at a given point in time. Due to the high dimensionality of the data, summarising mortality information is essential for various analyses, such as visualisation and clustering. We propose the use of beta latent variable (BLV) models to summarise mortality information without data transformation. A time-dependent version of the BLV model is developed by incorporating an autoregressive prior for the latent effects. This model aims to represent mortality data with a small set of $K$ latent effects while accounting for time dependence between these effects. Inference is performed using Bayesian methods, with posterior samples generated via Hamiltonian Monte Carlo. The BLV model is applied to probabilities of death from the Human Mortality Database, covering 41 countries and 23 age-specific probabilities of death over several periods. The time-dependent BLV model with $K=6$ latent effects accurately reconstructs observed mortality data, and the model parameters have intuitive and insightful interpretations. The time-dependent BLV outperforms the standard Gaussian factor analysis model applied to logit probability of death, and demonstrates that BLV models can effectively summarise mortality data.