In this data-intensive era, analyzing datasets with imbalanced binary responses is an important yet challenging task due to the common presence of outliers, heteroskedasticity, and other data anomalies. This talk introduces a novel and robust solution to improve the classification accuracies at various quantiles, with special focus on rare event detection applications, such as customer churn prediction, that are highly valuable to strategic business decision-making and profit maximization. Our proposed method first employs a hybrid data resampling approach that combines the benefits of both oversampling and undersampling, then imposes a Bayesian adaptive Lasso penalization on each quantile regression coefficient to perform statistical inference and variable selection simultaneously. Our resampling layer coupled with the Metropolis-Hastings-within-Gibbs algorithm is efficient and easy to implement. Extensive simulation studies and real data analyses showcase our competitive performance in comparison with some existing Bayesian methods in the literature.