Bayesian variable selection and model averaging in high-dimensional multinomial nonparametric regression

This article presents a Bayesian method for estimating nonparametrically a high-dimensional multinormal regression model. The regression functions are expressed as sums of main effects and interactions and our approach is able to select the significant components entering the model. Each of the main effects and interactions is written as a linear combination of basis terms with a variance components type prior on the regression coefficients. The conditional class probabilities are estimated using both variable selection and model averaging. Our approach can also be used for classification and gives results that are comparable to modem classification methods, but at the same time the results are highly interpretable to the practitioner. All computation is carried out using Markov chain Monte Carlo simulation.