Sains Malaysiana 55(8)(2026): 1393-1404

http://doi.org/10.17576/jsm-2026-5508-14

 

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

(Regresi Beta Kuantil Teratur Bayesian untuk Penganggaran Teguh dalam Data Pencong Terbatas)

 

FEDAA NOEEL ABDULAHAD^1,2, MAJID KHAN MAJAHAR ALI^2,* & ALAA ADNAN³

 

¹University of Al Hamdaniya, College of Education, Department of Mathematics, Mosul-Iraq

²School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

³University of Glasgow, James Watt School of Engineering, Glasgow, United Kingdom

 

Received: 26 November 2025/Accepted: 17 August 2026

 

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.

Keywords: Bayesian quantile regression; Beta distribution; robust regression; skewness

Abstrak

Taburan pencong selalunya mengandungi parameter bentuk yang menentukan arah dan magnitud asimetri. Dalam kes lain, kepencongan timbul secara semula jadi daripada bentuk taburan. Mengabaikan kepencongan semasa pemodelan dengan taburan simetri boleh menghasilkan inferens yang berat sebelah atau mengelirukan. Regresi kuantil terlaras Bayesian telah terbukti berkesan untuk tindak balas pencong, namun pendekatan sedia ada bergantung pada taburan Laplace asimetri (ALD), yang sokongan tidak terbatasnya menjadikan ia tidak sesuai untuk data terbatas. Untuk menangani batasan ini, kami mencadangkan model Regresi Beta Kuantil Teratur Bayesian (BRQBR) untuk menganalisis data terbatas yang disokong pada (0,1) dengan kepencongan yang wujud. Model yang dicadangkan menganggarkan kuantil bersyarat bagi tindak balas teragih Beta menggunakan rangka kerja teratur Bayesian berhierarki dengan prior pengecutan global-tempatan. Pensampel Gibbs dibangunkan untuk pengiraan posterior dan prestasi model dinilai di bawah tahap kepencongan dan senario pencemaran yang berbeza (5% dan 10% outlier) menggunakan taburan Beta dan logit-normal. Aplikasi pada set data pengeringan rumpai laut dunia sebenar menunjukkan peningkatan yang tekal dalam ketepatan ramalan. Merentasi simulasi dan analisis empirik, BRQBR mengatasi atau memadankan anggaran kemungkinan maksimum (MLE) sambil menunjukkan keteguhan yang kuat kepada pencilan. Rangka kerja yang dicadangkan menawarkan penyelesaian yang fleksibel dan tepat untuk memodelkan tindak balas pencong terbatas.

Kata kunci: Kepencongan; regresi kuantil bayesian; regresi teguh; taburan beta

 

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*Corresponding author; email: majidkhanmajaharali@usm.my