BAYESIAN QUANTILE REGRESSION WITH SUBSET SELECTION:A DECISION ANALYSIS PERSPECTIVE

• 成果类型: Article
• 署名作者: Feldman, Joseph; Kowal, Daniel R.
• 署名单位: Duke University; Cornell University; Rice University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157; 1941-7330
• DOI: 10.1214/25-AOAS2053
• 发表日期: 2025-09
• 页码: 2294-2319
• 关键词: VARIABLE SELECTION; decision theory; interpretable machine learning; Bayesian inference; variable selection; inference

摘要

Quantile regression is a powerful tool in epidemiological studies whereinterest lies in inferring how different exposures affect specific percentilesof the distribution of a health or life outcome. Existing methods either es-timate conditional quantiles separately for each quantile of interest or esti-mate the entire conditional distribution using semi- or nonparametric models.The former often produce inadequate models for real data and do not shareinformation across quantiles, while the latter are characterized by complexand constrained models that can be difficult to interpret and computationallyinefficient. Further, neither approach is well suited for quantile-specific sub-set selection. Instead, we pose the fundamental problems of linear quantileestimation, uncertainty quantification, and subset selection from a Bayesiandecision analysis perspective. For any Bayesian regression model, we deriveoptimal and interpretable linear estimates and uncertainty quantification foreach model-based conditional quantile. Our approach introduces a quantile-focused squared error loss, which enables efficient, closed-form computingand maintains a close relationship with Wasserstein-based density estimation.In an extensive simulation study, our methods demonstrate substantial gainsin quantile estimation accuracy, variable selection, and inference over fre-quentist and Bayesian competitors. We use these tools to identify and quantifythe heterogeneous impacts of multiple social stressors and environmental ex-posures on educational outcomes across the full spectrum of low- , medium- ,and high-achieving students in North Carolina.