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.

翻译：人口学家依赖多种工具和方法处理死亡率时间表——包括模型生命表、拟合方法、汇总指标预测以及预报，这些方法大多独立发展且未能提供结构一致的性别特异性输出。多维死亡率模型（MDMx）利用Tucker张量分解将上述四种功能统一于一体，并通过人类死亡率数据库（HMD）进行验证。HMD中的时期生命表被组织为logit(1qx)的四维张量，其索引维度为性别、年龄、国家及年份。通过共享性别与年龄因子矩阵，所有输出时间表在结构上天然保持一致性。由此分解衍生出四种功能：通过聚类与区域内部平滑轨迹构建模型生命表；采用三阶段算法与贝叶斯因子突变检测实现生命表拟合；通过汇总指标预测将儿童或成人死亡率映射为完整时间表，并在张量坐标下重构SVD-Comp方法；以及基于主成分分析缩减核心矩阵，采用阻尼局部线性趋势卡尔曼滤波器进行预报，其中包含层级漂移机制。