Adaptive Bayesian Quantile Regression for Count Data

Implements Bayesian quantile regression for count data using the jittering technique for discrete data smoothing and an asymmetric Laplace distribution likelihood. Supports adaptive variable selection via a random-bridge penalty with a beta prior on the power parameter, as well as fixed-bridge and Lasso penalties. Utilizes Markov chain Monte Carlo with Gibbs sampling and adaptive Metropolis-Hastings algorithms for posterior inference, provides Gelman-Rubin convergence diagnostics, and predicts conditional quantiles for count responses. Methodology and applications are based on the following key references: Luo, Zhou, Hu, and Li (2026, Journal of Mathematics, 2026:1543166, ), Koenker and Bassett (1978, Econometrica, 46, 33-50, ), Machado and Santos Silva (2005, Journal of the American Statistical Association, 100, 1226-1237, ), Yu and Moyeed (2001, Statistics and Probability Letters, 54, 437-447, ), Polson, Scott, and Windle (2014, Journal of the Royal Statistical Society Series B, 76, 713-733, ), Park and Casella (2008, Journal of the American Statistical Association, 103, 681-686, ), and Roberts and Rosenthal (2009, Journal of Computational and Graphical Statistics, 18, 349-367, ).