Bayesian analysis of the beta regression model subject to linear inequality restrictions with application

Year 2025, Volume: 54 Issue: 4, 1622 - 1636, 29.08.2025

Solmaz Seifollahi , Hossein Bevrani , Kristofer Månsson

https://doi.org/10.15672/hujms.1668576

Abstract

Recent studies in machine learning are based on models in which parameters or state variables are restricted by a restricted boundedness. These restrictions are based on prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. The valuable information contained in the restrictions must be considered during the estimation process to improve the accuracy of the estimation. Many researchers have focused on linear regression models subject to linear inequality restrictions, but generalized linear models have received little attention. In this paper, the parameters of beta Bayesian regression models subjected to linear inequality restrictions are estimated. The proposed Bayesian restricted estimator, which is demonstrated by simulated studies, outperforms ordinary estimators. Even in the presence of multicollinearity, it outperforms the ridge estimator in terms of the standard deviation and the mean squared error. The results confirm that the proposed Bayesian restricted estimator makes sparsity in parameter estimating without using the regularization penalty. Finally, a real data set is analyzed by the new proposed Bayesian estimation method.

Keywords

Bayesian inference , Beta regression model , Linear inequality restrictions , Link function , Restricted estimator

Ethical Statement

We certify that all authors have seen and approved the final version of the manuscript being submitted. They warrant that the paper is the authors' original work, hasn't received prior publication, and isn't under consideration for publication elsewhere.

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