  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.
