Handling Bounded Response in High Dimensions: a Horseshoe Prior Bayesian Beta Regression Approach
Year: 2025
Type: article
Abstract: Bounded continuous responses—such as proportions—arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the flexibility of the Beta distribution over the unit interval. While Bayesian extensions of Beta regression have shown promise, existing methods are limited to low-dimensional settings and lack theoretical guarantees. In this work, we propose a novel Bayesian approach for a high-dimensional sparse Beta regression framework that employs a tempered posterior. Our method incorporates the Horseshoe prior for effective shrinkage and variable selection. Most notably, we propose a novel Gibbs sampling algorithm using the Pólya-Gamma augmentation for efficient inference in Beta regression model. We also provide the first theoretical results establishing posterior consistency and convergence rates for Bayesian Beta regression. Through extensive simulation studies in both low- and high-dimensional scenarios, we demonstrate that our approach outperforms existing alternatives, offering improved estimation accuracy and model interpretability. Our method is implemented in the R package “betaregbayes” available on Github: https://github.com/tienmt/betaregbayes.
Source: Bayesian Analysis
DOI: 10.1214/26-ba1593
Author: The Tien Mai
Institution: Norwegian Institute of Public Health
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416048010
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