A Dirichlet-Multinomial-Poisson framework for the coherent analysis and forecast of cause-specific mortality

2026-03-01

AI Summary

This study addresses the incoherence commonly observed in cause-specific mortality models, where predicted deaths by cause often fail to sum to the total number of deaths. To resolve this, the authors propose a hierarchical probabilistic framework that, for the first time, integrates a Poisson–Dirichlet–multinomial structure into mortality modeling: a Poisson distribution models the total death count, a Dirichlet distribution captures the proportions of causes of death, and a multinomial distribution generates cause-specific death counts, thereby inherently ensuring coherence. Evaluated on U.S. and French mortality data from 1979 to 2023, the approach demonstrates high predictive accuracy and well-calibrated uncertainty for both aggregate and cause-specific forecasts, supports interpretable demographic pattern analysis, and maintains consistency across sexes and countries.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Separate modelling of cause specific mortality rates and their projections can yield inconsistent forecasts when the sum of deaths by cause does not match the total observed in a population. We develop a hierarchical probabilistic framework for cause specific mortality counts in which both the total number of deaths and the occurrence of deaths across causes are treated as random. Conditional on the total number of deaths, cause specific counts follow a multinomial distribution, whereas the total count is modelled using a Poisson distribution, and the vector of cause of death probabilities is assigned a Dirichlet distribution. The variation in cause specific mortality rates by age and calendar year is captured in both the Poisson and Dirichlet models, allowing interpretable demographic patterns while preserving coherence by construction. This model construction naturally preserves the coherence between the sum of deaths by cause and the total mortality. The method is exhibited through the analysis of cause specific mortality rates in the United States and France, sourced from the Human Mortality Database from 1979 to 2023, separately by sex and across ages, with deaths grouped into major cause categories. The empirical analysis uses a rolling 15 year out o fsample evaluation and compares the proposed model with the standard Lee Carter model and its compositional extension. The results show that coherent projections can be obtained across countries and sexes, that competitive predictive accuracy is achieved, and that uncertainty is well calibrated for both total and cause specific mortality.

Problem

• cause-specific mortality
• coherent forecasting
• mortality projection
• inconsistency
• demographic coherence

Innovation

• Dirichlet-Multinomial-Poisson
• coherent forecasting
• cause-specific mortality
• hierarchical probabilistic model
• mortality decomposition