Abstract Most of the existing probit classi?ers are based on sparsity-oriented modeling. However, we show that sparsity is not always desirable in practice, and only an appropriate degree of sparsity is pro?table. In this work, we propose a ?exible probabilistic model using a generalized Gaussian scale mixture prior that can promote an appropriate degree of sparsity for its model parameters, and yield either sparse or non-sparse estimates according to the intrinsic sparsity of features in a dataset. Model learning is carried out by an ef?cient modi?ed maximum a posteriori (MAP) estimate. We also show relationships of the proposed model to existing probit classi?ers as well as iteratively re-weighted l1 and l2 minimizations. Experiments demonstrate that the proposed method has better or comparable performances in feature selection for linear classi?ers as well as in kernel-based classi?cation.