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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 ABDULAHAD1,2, MAJID KHAN MAJAHAR ALI2,* & 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
Diserahkan: 26 November 2025/Diterima: 17 Ogos 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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*Pengarang untuk
surat-menyurat; email: majidkhanmajaharali@usm.my
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