Bayesian Estimation Approach for Linear Regression Models with Linear Inequality Restrictions

• Main Authors: Seifollahi, Solmaz, Kamary, Kaniav, Bevrani, Hossein
• Format: Journal Article
• Language: English
• Published: 06-12-2021
• Subjects: Statistics - Computation; Statistics - Methodology; Statistics - Other Statistics
• DOI: 10.48550/arxiv.2112.02950

Univariate and multivariate general linear regression models, subject to
linear inequality constraints, arise in many scientific applications. The
linear inequality restrictions on model parameters are often available from
phenomenological knowledge and motivated by machine learning applications of
high-consequence engineering systems (Agrell, 2019; Veiga and Marrel, 2012).
Some studies on the multiple linear models consider known linear combinations
of the regression coefficient parameters restricted between upper and lower
bounds. In the present paper, we consider both univariate and multivariate
general linear models subjected to this kind of linear restrictions. So far,
research on univariate cases based on Bayesian methods is all under the
condition that the coefficient matrix of the linear restrictions is a square
matrix of full rank. This condition is not, however, always feasible. Another
difficulty arises at the estimation step by implementing the Gibbs algorithm,
which exhibits, in most cases, slow convergence. This paper presents a Bayesian
method to estimate the regression parameters when the matrix of the constraints
providing the set of linear inequality restrictions undergoes no condition. For
the multivariate case, our Bayesian method estimates the regression parameters
when the number of the constrains is less than the number of the regression
coefficients in each multiple linear models. We examine the efficiency of our
Bayesian method through simulation studies for both univariate and multivariate
regressions. After that, we illustrate that the convergence of our algorithm is
relatively faster than the previous methods. Finally, we use our approach to
analyze two real datasets.