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

2026-03-27

AI Summary

This study addresses the challenge of effectively reducing and analyzing high-dimensional age-specific mortality probability data, which exhibits complex structural dependencies. The authors propose a time-dependent Beta latent variable model that, for the first time, incorporates an autoregressive prior to capture the temporal evolution of mortality rates. By modeling directly on the original probability scale without requiring a logit transformation, the approach enhances interpretability. Leveraging Bayesian inference with Hamiltonian Monte Carlo sampling, the model accurately reconstructs multi-country, multi-age mortality data using only six latent variables. This performance substantially surpasses that of conventional Gaussian factor analysis, and the inferred latent variables possess clear demographic interpretations.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• mortality data
• dimensionality reduction
• time dependence
• age-specific mortality
• data summarisation

Innovation

• beta latent variable model
• time-dependent modeling
• autoregressive prior
• Bayesian inference
• mortality data summarization