Bayesian Analysis of the Beta Regression Model Subject to Linear Inequality Restrictions with Application

• Main Authors: Seifollahi, Solmaz, Bevrani, Hossein, Mansson, Kristofer
• Format: Journal Article
• Language: English
• Published: 24-01-2024
• Subjects: Statistics - Computation; Statistics - Methodology
• DOI: 10.48550/arxiv.2401.13787

ReRecent studies in machine learning are based on models in which parameters
or state variables are bounded restricted. These restrictions are from 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
estimation accuracy. 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.