Multi-dimensional Mortality (MDMx): Sex-Age-Specific Model Life Tables, Fitting, Prediction from Summary Mortality Indicators, and Forecasting

TL;DR

The paper introduces MDMx, a unified tensor-based model that coherently integrates model life tables, fitting, prediction, and forecasting of mortality schedules, demonstrated with the Human Mortality Database.

Contribution

It develops a comprehensive tensor decomposition framework that unifies multiple mortality analysis tools into a single, coherent model with new algorithms for fitting and forecasting.

Findings

Unified tensor model for mortality schedules

Effective clustering and smoothing of life tables

Accurate mortality prediction and forecasting

Abstract

Demographers rely on a variety of tools and methods to work with mortality schedules - model life tables, fitting methods, summary-indicator prediction, and forecasting - largely developed independently and not providing structurally coherent sex-specific outputs. The multi-dimensional mortality model (MDMx) unifies all four within one Tucker tensor decomposition demonstrated using the Human Mortality Database (HMD). Period life tables from the HMD are organized as a four-way tensor of logit(1qx) indexed by sex, age, country, and year. Shared factor matrices for sex and age make every output schedule structurally coherent by construction. From this decomposition four capabilities emerge: model life tables via clustering and smooth within-regime trajectories; life table fitting via a three-stage algorithm with Bayes-factor disruption detection; summary-indicator prediction mapping child or adult mortality to complete schedules, reformulating SVD-Comp in tensor coordinates; and forecasting via a damped local linear trend Kalman filter on PCA-reduced core matrices with hierarchical drift.