In the era of big data, variable selection is a key technology for handling high-dimensional problems with a small sample size but a large number of covariables. Different variable selection methods were proposed for different models, such as linear model, logistic model and generalized linear model. However, fewer works focused on variable selection for single index models, especially, for single index logistic model, due to the difficulty arose from the unknown link function and the slow mixing rate of MCMC algorithm for traditional logistic model. In this paper, we proposed a Bayesian variable selection procedure for single index logistic model by taking the advantage of Gaussian process and data augmentation. Numerical results from simulations and real data analysis show the advantage of our method over the state of arts.
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