March 2024 Bayesian adaptive and interpretable functional regression for exposure profiles
Yunan Gao, Daniel R. Kowal
Author Affiliations +
Ann. Appl. Stat. 18(1): 642-663 (March 2024). DOI: 10.1214/23-AOAS1805


Pollutant exposure during gestation is a known and adverse factor for birth and health outcomes. However, the links between prenatal air pollution exposures and educational outcomes are less clear, in particular, the critical windows of susceptibility during pregnancy. Using a large cohort of students in North Carolina, we study the link between prenatal daily PM2.5 exposure and fourth end-of-grade reading scores. We develop and apply a locally adaptive and highly scalable Bayesian regression model for scalar responses with functional and scalar predictors. The proposed model pairs a B-spline basis expansion with dynamic shrinkage priors to capture both smooth and rapidly-changing features in the regression surface. The model is accompanied by a new decision analysis approach for functional regression that extracts the critical windows of susceptibility and guides the model interpretations. These tools help to identify and address broad limitations with the interpretability of functional regression models. Simulation studies demonstrate more accurate point estimation, more precise uncertainty quantification, and far superior window selection than existing approaches. Leveraging the proposed modeling, computational, and decision analysis framework, we conclude that prenatal PM2.5 exposure during early and late pregnancy is most adverse for fourth end-of-grade reading scores.

Funding Statement

Research was sponsored by the Army Research Office (W911NF-20-1-0184), the National Institute of Environmental Health Sciences of the National Institutes of Health (R01ES028819), and the National Science Foundation (SES-2214726). The content, views, and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office, the North Carolina Department of Health and Human Services, Division of Public Health, the National Institutes of Health, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein.


The authors would like to thank the review team for their constructive comments and Dr. Mercedes Bravo, Dr. Katherine B. Ensor, and Dr. Marie Lynn Miranda for their valuable insights.


Download Citation

Yunan Gao. Daniel R. Kowal. "Bayesian adaptive and interpretable functional regression for exposure profiles." Ann. Appl. Stat. 18 (1) 642 - 663, March 2024.


Received: 1 October 2022; Revised: 1 May 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1805

Keywords: decision analysis , Functional data analysis , Nonparametric regression , shrinkage , Spline

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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