On the Bayesian multidimensional-matrix polynomial empirical regression

Abstract

The problem of the parameters estima-tion for the polynomial in the input variables regression function is formu-lated and solved. The input and output variables of the regression function are multidimensional-matrices. The pa-rameters of the regression function are assumed to be random independent multidimensional matrices with Gauss-ian distribution and known mean value and dispersion matrices. The solution to this problem is a multidimensional-matrix system of the linear algebraic equations in multidimensional-matrix unknowns – function regression pa-rameters. We have considered particu-lar case of quadratic regression func-tion, for which we have obtained for-mulas for parameters calculation. The computer simulation of the quadratic regression functions is performed for the two-dimensional matrix input and output variables.