Suggesting an algorithm for estimating the parameters of a linear regression model, Bayesian approximation computation ABC with Gibbs sampler algorithm

الملخص

The concept of linear regression model has been developed to address complex types of studied phenomena, these phenomena have been modeled using fuzzy linear with crisp inputs and fuzzy outputs, and to estimate the parameters of this model we have two methods: possibilistic and least squares methods.

In this paper, we have proposed an algorithm that combines possibilistic and least squares methods to find the fuzzy linear regression coefficients by applying the Bayesian Method , which notes the random nature of phenomena and has a high predictive ability, by merging the Gibbs sampler algorithm with the Bayesian approximation algorithm, and assuming the initial values ​​and distributions prior.

Its quality was verified by applying it to real and generated data, and the results were compared with Tanaka possibilistic model and least squares methods (Zeng's model) using the Quality of Fit (GOF) scale.

The results of the research indicated that the proposed algorithm gives the best accuracy for estimating the coefficients of the fuzzy linear regression model, and it also overcame the problem of determining the likelihood function in the fuzzy model and in determining the prior distributions.