Bayesian analysis of high-dimensional gene expression using semiparametric quantile regression

High-dimensional gene expression studies often exhibit heterogeneity, nonlinear effects, and distributional shifts that cannot be captured by mean regression methods. We propose a Bayesian Semiparametric Quantile Regression (BSQR) framework that integrates Gaussian process priors for nonlinear modeling with sparsity-inducing priors for variable selection. Relevant genes are identified using posterior inclusion probabilities (PIPs) and effect size thresholds, ensuring principled inference with false discovery control. Extensive simulations show that BSQR consistently outperforms Koenker's penalized B-spline quantile regression (B-SP) in terms of precision, recall, probability calibration, and robustness under nonlinear and heteroskedastic conditions. In particular, BSQR achieves higher AUCs, lower Brier scores, and more stable gene discovery across quantiles. Application to the GSE2034 breast cancer dataset confirms these advantages, yielding substantial improvements in discrimination, calibration, and selection reliability. Overall, BSQR provides a flexible and powerful framework for quantile-specific genomic analysis in high-dimensional settings.