A0586
Title: General Bayesian quantile regression of count via generative modeling
Authors: Yuta Yamauchi - Nagoya University (Japan) [presenting]
Genya Kobayashi - Meiji University (Japan)
Shonosuke Sugasawa - Keio University (Japan)
Abstract: Quantile regression is a powerful tool for understanding the distribution of a response variable conditioned on explanatory variables, yet its application to count data remains challenging due to discreteness and model inflexibility. A novel Bayesian quantile regression method is proposed for count data that overcomes these limitations by nonparametrically modeling the joint distribution of latent responses and covariates. A continuous latent variable is introduced to associate with the discrete response, and the joint distribution of the latent variable and covariates is modeled nonparametrically using a Pitman-Yor process mixture. This approach enables flexible modeling of the conditional distribution without restrictive parametric assumptions. Conditional quantiles are derived from the joint distribution, and regression effects are inferred through general Bayesian updating. Simulation studies and real data analysis demonstrate that the method significantly outperforms existing techniques, including jittering and continuous Poisson regression, in accurately capturing conditional quantiles and their covariate dependencies. This framework enables accurate estimation of conditional quantiles and flexible modeling of covariate effects, particularly when the underlying distribution of count data is complex or deviates from standard assumptions.
