基于贝叶斯方法的比例数据分位数推断及其应用

为了尝试使用贝叶斯方法研究比例数据的分位数回归统计推断问题,首先基于Tobit模型给出了分位数回归建模方法,然后通过选取合适的先验分布得到了贝叶斯层次模型,进而给出了各参数的后验分布并用于Gibbs抽样。数值模拟分析验证了所提出的贝叶斯推断方法对于比例数据分析的有效性。最后,将贝叶斯方法应用于美国加州海洛因吸毒数据,在不同的分位数水平下揭示了吸毒频率的影响因素。

Bayesian Inference for Quantile Regression of Proportional Data and Its Application

In this paper,we try to use Bayesian method to investigate the regression modeling of the proportional data in the framework of quantile regression.We first give the proposed quantile regression for proportional data based on Tobit model,and then obtain the Bayesian hierarchical model through choosing appropriate prior distributions,which lead to the posterior distribution for Gibbs sampling method.The usefulness and good performance of our proposed method is examined by the simulation studies.Finally,we apply newly proposed method to the heroin use data in California,and reveal the influence factors of drug use frequency at different quantile levels.