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.
翻译:在许多科学应用中,都存在受线性不平等制约的单向和多变一般线性回归模型。对模型参数的线性不平等限制,往往来自苯蛋学知识,其动机是高序列工程系统的机器学习应用(Agrell, 2019年;Veiga和Marrel,2012年)。关于多个线性模型的一些研究考虑到在上界和下界之间限制的回归系数参数已知的线性组合。在本文件中,我们考虑了受这种线性限制的单向和多变量一般线性模型。迄今为止,基于Bayesian方法的单向线性案例研究,其条件是线性限制的系数矩阵是完全级的平方矩阵。然而,这一条件并非永远可行。另一个困难在于通过采用Gibbs算法来估计已知的线性参数的线性组合。本文用一种巴伊斯方法来估计回归参数,当提供线性不平等限制的制约的制约方法的矩阵矩阵的矩阵时。对于基于Bayesian方法的单向全线性案例的研究,我们用两种方法的递性矩阵的递性矩阵的回归性参数来评估我们通过两种递增法的递增法的数值。我们两个模型的递增的数值是我们之前的递增法的递增的数值。我们两个的递增法的递制的方法。