A New Robust Binary Bayesian LASSO

ABSTRACT The robustness of Bayesian variable selection with Laplacian likelihood has been demonstrated in binary classification scenarios when latent continuous responses are contaminated with outliers and follow heavy‐tailed distributions. Nevertheless, published studies in this category typically adopt Laplacian shrinkage priors for regularized estimation and variable selection, which lead to inaccuracy since exact sparse parameter estimates cannot be induced directly. In this paper, we propose a Bayesian hierarchical model for robust binary LASSO with spike‐and‐slab priors to overcome limitations in existing shrinkage priors. Efficient posterior sampling can be conducted using the Gibbs sampler. We perform simulation studies to show the advantage of the new binary least absolute deviation (LAD) Bayesian LASSO compared with benchmarks. In a case study of diabetes data under a binary response, the proposed method yields better variable selection and classification results compared to alternatives.