带有不可忽略缺失数据的半参数再生散度模型的贝叶斯分析

半参数再生散度模型是再生散度模型和半参数回归模型的推广,包括了半参数广义线性模型和广义部分线性模型等特殊类型.讨论的是该模型在响应变量和协变量均存在非随机缺失数据情形下参数的Bayes估计和基于Bayes因子的模型选择问题.在分析中,采用了惩罚样条来估计模型中的非参数成分,并建立了Bayes层次模型;为了解决Gibbs抽样过程中因参数高度相关带来的混合性差以及因维数增加导致出现不稳定性的问题,引入了潜变量做为添加数据并应用了压缩Gibbs抽样方法,改进了收敛性;同时,为了避免计算多重积分,利用了M-H算法估计边缘密度函数后计算Bayes因子,为模型的选择比较提供了一种准则.最后,通过模拟和实例验证了所给方法的有效性.

BAYESIAN ANALYSIS FOR SEMIPARAMETRIC REPRODUCTIVE DISPERSION MODELS WITH NONIGNORABLY MISSING DATA

Semiparametric reproductive dispersion model (SRDNM) is an extension of reproductive dispersion models and semiparametric regression models, and includes generalized partial linear model and semiparametric generalized linear model as its special cases. A method is proposed to obtain Bayesian estimationand to select appropriate model based on Bayes factor for such modelwith missing data both in covariate and response. Firstly, nonparametric components are fitted by penalized-splines and a Bayesian hierarchical model is set to model smooth parameters, then latent variables are introduced and the collapsed Gibbs sampler is implemented in order to improve the mixing androbustness of MCMC. Finally, simulation and real datasets are presented to illustrate the proposed methods.