贝叶斯统计和经典统计在分位数回归分析中的比较  

Comparison of Bayesian statistics and classical statistics in quantile regression analysis

作　　者：谷恒明 胡良平 GU Heng-ming;HU Liang-ping(Consulting Center for Biomedical Statistics, Graduate School, Academy of Military Sciences, Beijing 100850, China;Specialty Committee of Clinical Scientific Research Statistics,World Federation of Chinese Medicine Societies, Beijing 100029, China)

机构地区：[1]军事科学院研究生院生物医学统计学咨询中心,北京100850 [2]世界中医药学会联合会临床科研统计学专业委员会,北京100029

出　　处：《军事医学》2018年第2期149-153,共5页Military Medical Sciences

基　　金：国家高技术研究发展计划资助项目(2015AA020102)

摘　　要：目的在分位数回归分析中比较贝叶斯统计和经典统计,以便在不同场合下选择更加有效的方法。方法选择大样本数据,基于经典统计和贝叶斯统计的分位数回归分析利用SAS软件中的QUANTREG过程和MCMC过程实现。分别采用十折交叉验证方法,通过训练集的拟合效果和预测集的预测效果两方面来评价模型优劣。结果若采用全部样本建立模型时,基于经典统计的分位数回归分析评价指标略差于基于贝叶斯统计的分位数回归分析评价指标;基于部分样本作为训练集的十折交叉验证时,比较10次指标的均值,基于贝叶斯统计相对于基于经典统计而言,在具体的分位数回归方程中,其下四分位数(Q1)和上四分位数(Q3)的拟合效果为优,而中位数(Q2)的拟合效果略差;对于预测效果而言,基于贝叶斯统计的分位数回归方程要优于经典统计的分位数回归方程。结论在拟解决实际问题的场合下,如要求准确度较高,主要考察各个分位数预测效果和拟合效果,可选择贝叶斯分位数回归分析法;若主要考察中位数的拟合效果则需要谨慎选择。如时间精力有限且样本量足够大,那么采用经典统计的分位数回归分析即可。Objective To compare the Bayesian statistics and the classical statistics in the quantile regression analysis in order to select a more effective method. Methods The large sample data was chosen,and the QUANTREG procedure in SAS was used for the classical statistics and the MCMC procedure in SAS for the Bayesian one,respectively. Using ten-fold cross-validation method,the goodness of fitting of the models was appraised in terms of the fitted effect based on the training dataset and the predicted effect based on the predictive dataset. Results In most cases,the indexes of the quantile regression models in the classical statistics were slightly worse than those of the Bayesian one. In the ten-fold crossvalidation of the partial samples as a training dataset,the fitting effect of the lower quartile（ Q1） and upper quartile（ Q3）of the Bayesian statistics was better than that of the classical one. However,the median（ Q2） fitting effect of the Bayesian statistics was slightly worse than that of the classical one. As for the prediction effect,the Bayesian statistical quantile regression model was superior to the classic one. Conclusion To expect high accuracy,such as the predictive effects and fitting effects of each quantile,the Bayesian quantile regression analysis should be chosen. If the major concern is the fitting effect of the median,careful selection from the approaches mentioned above is needed. If time and energy are limited,and the sample size is large enough,the classic statistical quantile regression analysis is a good choice.

关 键 词：贝叶斯统计 经典统计 分位数回归 拟合效果 预测效果 交叉验证 

分 类 号：C8[社会学—统计学]