Spatially-Indexed Longitudinal Distributional Outcome Regression for Environmental Monitoring

2026-09-14

AI Summary

该研究提出了一种新的空间索引纵向分布结果回归模型，使用贝塞尔基多项式和样条张量积扩展来解决环境监测中时空依赖性和数学约束问题。

Abstract

Characterizing longitudinal changes in region-specific distribution of environmental exposures, such as total nitrate (TNO$_3$) concentrations, is critical for understanding localized ecological risks that are otherwise obscured by standard mean-level modeling. However, modeling longitudinal distributional outcomes across spatial regions presents significant methodological challenges. The random objects are spatio-temporally dependent, and mathematical constraints are inherent to distributional representations, such as, monotonicity of quantile functions. To address this, we propose a novel spatially-indexed longitudinal distributional outcome regression model. The distributional coefficients corresponding to the fixed effects of covariates are modeled using Bernstein basis polynomials, while spatio-temporal random effects are flexibly captured via tensor product expansions of splines. We develop a scalable Markov Chain Monte Carlo (MCMC) algorithm to explicitly account for spatial dependencies, and introduce a fast two-stage projected-posterior approach to preserve the monotonicity of the predicted subject-specific quantile functions. Extensive simulation studies demonstrate that the proposed framework achieves superior estimation accuracy and predictive performance compared to standard non-spatial distributional outcome regression. We apply our methodology to predict monthly, site-specific distributions of TNO$_3$ concentrations across the contiguous United States. Accounting for spatial correlation provides substantially lower uncertainty in the estimated distributional effects and improves predictive performance over the non-spatial alternative, offering a robust, interpretable tool for spatio-temporal environmental monitoring.

Problem

• Environmental Monitoring
• Longitudinal Distributional Outcome
• Spatio-temporal Dependence

Innovation

• Spatially-Indexed Longitudinal Distributional Outcome Regression
• Bernstein Basis Polynomials
• Tensor Product Expansions of Splines
• Markov Chain Monte Carlo (MCMC)
• Projected-Posterior Approach