Bayesian Regularized Quantile Beta Regression for Robust Estimation in Skewed Bounded Data

Abstract

Skewed distributions often contain shape parameters that determine the direction and magnitude of asymmetry. In other cases, skewness arises naturally from the form of the distribution. Ignoring skewness when modeling with symmetric distributions may yield biased or misleading inferences. Bayesian regularized quantile regression has proven effective for skewed responses, yet existing approaches rely on the asymmetric Laplace distribution (ALD), whose unbounded support makes it unsuitable for bounded data. To address this limitation, we propose a Bayesian Regularized Quantile Beta Regression (BRQBR) model for analyzing bounded data supported on (0,1) with inherent skewness. The proposed model estimates conditional quantiles of a Beta-distributed response using a hierarchical Bayesian regularization framework with global–local shrinkage priors. A Gibbs sampler is developed for posterior computation, and the model's performance is evaluated under different skewness levels and contamination scenarios (5% and 10% outliers) using Beta and logit-normal distributions. Application to a real-world seaweed drying dataset demonstrates consistent improvements in predictive accuracy. Across simulation and empirical analysis, BRQBR outperforms or matches maximum likelihood estimation (MLE) while exhibiting strong robustness to outliers. The proposed framework offers a flexible and accurate solution for modeling skewed bounded responses.