Bayesian mortality forecasting with a Conway--Maxwell--Poisson specification

2026-01-04

AI Summary

This study addresses the limitations of traditional mortality models in adequately capturing dispersion patterns—such as overdispersion or underdispersion—in death count data, which hinders accurate characterization of variability. To overcome this, the authors introduce the Conway–Maxwell–Poisson (CMP) distribution into a Bayesian stochastic mortality modeling framework for the first time, treating the dispersion parameter as an unknown quantity. By assigning a Gamma prior, the approach coherently integrates parameter, process, and distributional uncertainties within a unified inferential structure, with posterior inference conducted via Markov chain Monte Carlo (MCMC) methods. The resulting model flexibly accommodates underdispersed, equidispersed, and overdispersed scenarios. Empirical analysis using male mortality data from England and Wales demonstrates that the proposed model significantly outperforms conventional Poisson and negative binomial models in both goodness-of-fit and predictive accuracy, with particularly pronounced advantages in overdispersed settings.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Bayesian LearningCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systemsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Models for Web evolution

Abstract

This paper presents a novel approach to stochastic mortality modelling by using the Conway--Maxwell--Poisson (CMP) distribution to model death counts. Unlike standard Poisson or negative binomial distributions, the CMP is a more adaptable choice because it can account for different levels of variability in the data, a feature known as dispersion. Specifically, it can handle data that are underdispersed (less variable than expected), equidispersed (as variable as expected), and overdispersed (more variable than expected). We develop a Bayesian formulation that treats the dispersion level as an unknown parameter, using a Gamma prior to enable a robust and coherent integration of the parameter, process, and distributional uncertainty. The model is calibrated using Markov chain Monte Carlo (MCMC) methods, with model performance evaluated using standard statistical criteria such as residual analysis and scoring rules. An empirical study using England and Wales male mortality data shows that our CMP-based models provide a better fit for both existing data and future predictions compared to traditional Poisson and negative binomial models, particularly when the data exhibit overdispersion. Finally, we conduct a sensitivity analysis with respect to prior specification to assess robustness.

Problem

• mortality forecasting
• overdispersion
• underdispersion
• stochastic mortality modelling
• dispersion

Innovation

• Conway–Maxwell–Poisson
• Bayesian mortality forecasting
• overdispersion
• Markov chain Monte Carlo
• stochastic mortality modelling