偏正态数据下半参数混合效应模型的贝叶斯估计  

Bayesian Estimation of Semi-parametric Mixed Effect Model under Skew-normal Data

作　　者：郑丛平 王涛 谢有余 ZHENG Congping;WANG Tao;XIE Youyu(School of Mathematics,Yunnan Normal University,Kunming 650091,China)

机构地区：[1]云南师范大学数学学院,昆明650091

出　　处：《重庆工商大学学报（自然科学版）》2023年第4期93-98,共6页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(81360449);云南省教育厅科学研究基金项目(2022Y187);云南师范大学研究生科研创新基金(YJSJJ22-B95).

摘　　要：针对纵向数据服从非正态分布情况下混合效应模型的估计问题,提出偏正态分布半参数混合效应模型的贝叶斯估计方法;假定个体测量误差服从偏正态分布,纵向指标与时间的关系采用B样条方法建模,在共轭先验下考虑该模型的贝叶斯分析,基于MH算法与Gibbs抽样的混合算法获取未知参数、随机效应和非参数函数的贝叶斯估计;数值模拟中,数据非正态分布条件下将偏正态方法得到的估计与传统半参数混合效应模型估计方法进行对比,发现偏正态半参数混合效应模型在有限样本情况下表现更好,说明偏正态半参数混合效应模型与传统模型相比,可以更好地拟合偏态数据,获得更加精准的参数估计;最后将该方法应用于ADNI数据中,研究了神经评分与基线临床指标间的关系,得出了合理的结论,证明了方法的合理性。Aiming at the estimation problem of the mixed effect model when longitudinal data obey non-normal distribution,a Bayesian estimation method of semi-parametric mixed effect model with skew-normal distribution was proposed.Individual measurement error obeys skew-normal distribution,and the relationship between longitudinal index and time was modeled by B spline method.Bayesian analysis of the model was considered under conjugate prior,and Bayesian estimation of unknown parameters,random effects and nonparametric functions was obtained based on the mixed algorithm of MH algorithm and Gibbs sampling.In the numerical simulation,under the condition of non-normal distribution of data,the estimation obtained by the skew-normal method was compared with that of the traditional semi-parametric mixed effect model.It is found that the skew-normal semiparametric mixed effect model performs better under the condition of limited samples,which indicates that the skew-normal semiparametric mixed effect model can better fit the skewed data than the traditional model,and the Bayesian method can effectively use prior information to obtain more accurate parameter estimation.Finally,the modified method was applied to ADNI data,and the relationship between neural score and baseline clinical indicators was studied.A reasonable conclusion was drawn,which proved the rationality of the method.

关 键 词：偏正态分布 B样条 混合效应模型 贝叶斯估计 ADNI数据 

分 类 号：O212.8[理学—概率论与数理统计]