Although quantile regression has emerged as a powerful tool for understanding various quantiles of a response variable conditioned on a set of covariates, the development of quantile regression for count responses has received far less attention. This paper proposes a new Bayesian approach to quantile regression for count data, which provides a more flexible and interpretable alternative to the existing approaches. The proposed approach associates the continuous latent variable with the discrete response and nonparametrically estimates the joint distribution of the latent variable and a set of covariates. Then, by regressing the estimated continuous conditional quantile on the covariates, the posterior distributions of the covariate effects on the conditional quantiles are obtained through general Bayesian updating via simple optimization. The simulation study and real data analysis demonstrate that the proposed method overcomes the existing limitations and enhances quantile estimation and interpretation of variable relationships, making it a valuable tool for practitioners handling count data.

翻译：尽管分位数回归已成为理解响应变量在给定协变量条件下各种分位数的有力工具，但针对计数响应变量的分位数回归方法发展却鲜受关注。本文提出一种新的贝叶斯计数数据分位数回归方法，为现有方法提供了更灵活且可解释的替代方案。该方法通过连续潜变量与离散响应变量建立关联，并以非参数方式估计潜变量与协变量集的联合分布。随后，通过将估计的连续条件分位数对协变量进行回归，借助基于简单优化的通用贝叶斯更新机制，可获得协变量对条件分位数影响的后验分布。仿真研究与实际数据分析表明，所提方法克服了现有局限，提升了分位数估计与变量关系解释能力，使其成为处理计数数据的实践者的重要工具。