纵向数据下半参数联合均值协方差模型的贝叶斯分析  

Bayesian analysis for semiparametric joint mean-covariance models with longitudinal data

作　　者：田瑞琴 赵远英[2] 徐登可[3] TIAN Rui-qin;ZHAO Yuan-ying;XU Deng-ke(School of Sicience,Hangzhou Normal University,Hangzhou 311121,China;College of Mathematics and Information Science,Guiyang University,Guiyang 550005,China;Department of Statistics,Zhejiang Agriculture and Forestry University,Hangzhou 311300,China)

机构地区：[1]杭州师范大学理学院,浙江杭州311121 [2]贵阳学院数学与信息科学学院,贵州贵阳550005 [3]浙江农林大学统计系,浙江杭州311300

出　　处：《高校应用数学学报（A辑）》2021年第1期21-35,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11801514,11761016);浙江省统计重点研究项目(20TJZZ13);杭州师范大学科研启动项目(2019QDL039)。

摘　　要：基于改进的Cholesky分解,研究分析了纵向数据下半参数联合均值协方差模型的贝叶斯估计和贝叶斯统计诊断,其中非参数部分采用B样条逼近.主要通过应用Gibbs抽样和Metropolis-Hastings算法相结合的混合算法获得模型中未知参数的贝叶斯估计和贝叶斯数据删除影响诊断统计量.并利用诊断统计量的大小来识别数据的异常点.模拟研究和实例分析都表明提出的贝叶斯估计和诊断方法是可行有效的.Based on the modified Cholesky decomposition,Bayesian estimation and Bayesian statistical diagnosis of semiparametric joint mean-covariance models with longitudinal data are studied.The nonparametric part is approximated by B-spline.The Bayesian estimation of unknown parameters and Bayesian case deletion influence diagnosis statistics in the models are obtained by using the hybrid algorithm of Gibbs sampling and Metropolis-Hastings algorithm.Then the abnormal points of data can be identified using the values of diagnostic statistics.Simulation study and real data analysis show that the proposed Bayesian estimation and diagnosis method is feasible and effective.

关 键 词：纵向数据 CHOLESKY分解 GIBBS抽样 Metropolis-Hastings算法 贝叶斯诊断 

分 类 号：O212.8[理学—概率论与数理统计]