Constructing prediction intervals for the age distribution of deaths

2025-06-22

AI Summary

This paper addresses the challenging problem of constructing prediction intervals for age-at-death distributions—functions that are nonnegative, subject to integral constraints (unit total probability), and often contain zeros. We propose a model-agnostic functional prediction interval framework. Methodologically, it jointly applies the centered log-ratio transformation and cumulative distribution function transformation to simultaneously alleviate nonnegativity, unit-integral, and zero-value constraints. Pointwise prediction intervals are then calibrated on a validation set using empirical coverage probability. The framework is compatible with arbitrary functional time series models and substantially improves interval reliability under sparse or constrained data regimes. Empirical evaluation on Japanese sex-specific mortality data demonstrates that, across multiple base models, the achieved coverage consistently approaches the nominal level (e.g., 95%), while yielding narrower average interval widths and markedly enhanced accuracy and robustness.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We introduce a model-agnostic procedure to construct prediction intervals for the age distribution of deaths. The age distribution of deaths is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation and a cumulative distribution function transformation are used to remove the two constraints, where the latter transformation can also handle the presence of zero counts. Our general procedure divides data samples into training, validation, and testing sets. Within the validation set, we can select an optimal tuning parameter by calibrating the empirical coverage probabilities to be close to their nominal ones. With the selected optimal tuning parameter, we then construct the pointwise prediction intervals using the same models for the holdout data in the testing set. Using Japanese age- and sex-specific life-table death counts, we assess and evaluate the interval forecast accuracy with a suite of functional time-series models.

Problem

• Construct prediction intervals for age-specific death distributions
• Handle constrained data with nonnegative and integral constraints
• Assess forecast accuracy using functional time-series models

Innovation

• Model-agnostic procedure for prediction intervals
• Log-ratio and CDF transformations for constraints
• Functional time-series models for accuracy assessment