Adaptive Bayesian Quantile Regression for Count Data: A Random-Bridge Penalty Approach With Applications

A Bayesian modeling framework with a random-bridge prior is proposed for quantile regression of high-dimensional count data, addressing challenges in variable sparsity identification and model adaptability. Traditional approaches struggle with noise sensitivity and parameter inflexibility when handling discrete count data. The new method treats the penalty parameter as random with a prior distribution, enabling dynamic learning and adaptive adjustment of sparse structures. By incorporating jittering to manage data discreteness and building on the asymmetric Laplace distribution for likelihood construction, the framework employs an efficient Markov chain Monte Carlo algorithm that integrates Gibbs sampling with Metropolis–Hastings for posterior inference. Simulations across diverse data generation mechanisms show the method’s superiority over fixed-bridge penalty and Bayesian Lasso alternatives in variable selection accuracy, model stability, and estimation precision. Real-data applications further demonstrate its effectiveness in identifying key predictors across quantile levels, offering a flexible and robust Bayesian approach for quantile modeling of high-dimensional count data.