偏正态非线性再生散度随机效应模型的贝叶斯分析  

Bayesian Inference for Skew-Normal Nonlinear Reproductive Dispersion Mixed-Effect Models

作　　者：和燕[1] 唐年胜[2] 

机构地区：[1]楚雄师范学院计算机科学系,云南楚雄675000 [2]云南大学统计系,云南昆明650091

出　　处：《生物数学学报》2013年第3期563-575,共13页Journal of Biomathematics

基　　金：国家自然科学基金资助项目(109610256);云南省教育厅科研基金资助项目(06Y046F);楚雄师院科研骨干项目(200614)

摘　　要：非线性再生散度随机效应模型是一类非常广泛的统计模型,包括了广义线性随机效应模型和指数族非线性随机效应模型等.由于它更能灵活地刻画不同个体间的相关和联系,经常被用来模拟重复测量数据,对该模型传统的方法是假设随机效应服从正态分布.但对许多数据集的分析发现这样的假设有时不符合实际情况,会导致结论偏离真实.本文引入偏正态非线性再生散度随机效应模型,目的在于用一个偏正态分布来改进随机效应正态分布的假设,该分布包括了正态分布.同时结合Gibbs抽样技术和Metropolis-Hastings算法(简称MH算法)的混合算法获得了模型参数与随机效应的贝叶斯估计.一个模拟研究和一个HIV监测数据的研究用来说明上述算法的有效性.Nonlinear reproductive dispersion mixed models which are widely applied include generalized linear mixed models and exponential family mixed models etc.They are frequently used to analyze repeated measures data,because they are more flexible to modelling the correlation within-subject.The most popular method assumes the random effects are normally distributed,which can be an unrealistic assumption,obscuring important features of the variations present within and among the units.This paper presents skew-normal nonlinear reproductive dispersion mixed models（SN-NRDMM） that relax the normality assumption by using a multivariate skew-normal distribution,which includes the normal ones.A hybrid algorithm that combines Gibbs sampler and Metropolis-Hastings（MH） algorithm is implemented to produce the Bayesian estimates of Parameters and random effects.A simulation study and a real data set from a HIV monitoring data study are used to illustrate the methodology.

关 键 词：偏正态非线性再生散度随机效应模型 GIBBS抽样 MH算法 贝叶斯分析 MCMC 

分 类 号：O212.1[理学—概率论与数理统计]