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Novel Bayesian Model Class Selection for Regression Problems
  • Gilberto A. Ortiz
Gilberto A. Ortiz

Corresponding Author:[email protected]

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Abstract

Bayesian model class selection has attracted considerable interest in various research areas for the determination of the most plausible model class based on input/output measurements. Regression analysis is one of the areas in which Bayesian inference and Bayesian model class selection have been applied but it is not a trivial task to define due to the complex relation between input/output variables. It has been noted that the prior distribution of the regression coefficients affect the model class selection results. In this paper we propose a novel Bayesian nonparametric regression method using a popular nonparametric technique known as General Regression Neural Network. First, the General Regression Neural Network methodology is introduced. Then, Bayesian inference will be used to compute the optimal value of the smoothing parameter and the prediction-error variance, which are the only unknown parameters in the proposed procedure. Finally, Bayesian model class selection with a subjective influence of the prior will be used to identify the optimal set of design variables. The proposed method is assessed and validated through simulated and real applications.