On applying Monte Carlo methods to analysis of nonlinear regression models
Georgy Igorevich Rudoy
Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS, Vavilov St. 40, 119333, Moscow, Russia
Keywords: символьная регрессия, нелинейные модели, устойчивость решений, дисперсия прозрачной среды, методы класса Монте-Карло, symbolic regression, nonlinear models, solution stability, transparent medium dispersion, Monte Carlo methods
Abstract
This paper presents a criterium, called the coefficients stability for inaccuracy in determining the coefficients of nonlinear regression models describing inexact data. A method for the coefficients stability estimation is also described. The proposed criterium is illustrated by a computational experiment with the data obtained by measurements of a refractive index dependence on the wavelength in 400−1000 nm band for a transparent polymer. The convergence of the proposed criterium to the known analytical solution for the case of linear regression is also studied.
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