Proposing a new method to find the coefficients of the linear regression model using fuzzy Bayes method (Journal of Hama University, 2024)
In this paper, a method has been proposed to estimate the linear regression parameters in the presence of inaccurate a priori information about the parameters by combining the Bayes method and fuzzy logic, assuming fuzzy normal a priori distributions of the parameters, and has been obtained fuzzy estimates for the parameters. An algorithm has been also proposed to remove the blur that be noticed the randomness of the studied phenomena and is characterized by a high predictive ability, by proposing a distance function (stop condition) that provides a solution to the hyper-fitness of the model when using a quadratic distance function. The effectiveness of the proposed method has been verified by applying it to generated and realistic data, and the results have been compared to methods of least squares and deterministic Bayes in estimating based on two error criteria, MSE and MAE. The proposed method has been given the best accuracy for point estimating the coefficients of the linear regression model, and it also has overcome the problem of determining the prior probability distributions in the presence of inaccurate information about the parameters. least squares and deterministic bayes.
Keywords: linear regression model; Bayesian Method; Fuzzy Random Variables; fuzzy interval; Mrejection ABC (approximate Bayesian computation) algorith; Gibbs sampler algorithm