Bayesian variable selection for breast cancer: LASSO and Horseshoe priors

High-dimensional genomic data present significant challenges for variable selection and prediction, particularly when the number of predictors far exceeds the number of observations. Bayesian shrinkage priors offer a principled approach for addressing these challenges by inducing sparsity and enabling uncertainty quantification. In this study, we compare the performance of two prominent Bayesian priors the Bayesian LASSO and the Horseshoe prior within a logistic regression framework for binary classification. Through an extensive simulation study under both independent and correlated predictor settings, we evaluate each method’s ability to recover sparse signals and maintain estimation accuracy. We further apply both models to a real breast cancer gene expression dataset obtained from The Cancer Genome Atlas (TCGA) and GenBank. Model performance is assessed based on predictive accuracy, area under the ROC curve (AUC), and the biological relevance of selected genes. Our findings highlight the potential of global-local shrinkage priors, such as the Horseshoe, for robust and interpretable modeling in high-dimensional biomedical applications.