带有不可忽略缺失数据的混合线性模型的贝叶斯统计推断

发布时间：2018-06-12 05:01

本文选题：混合线性模型 + 不可忽略缺失数据　；参考：《云南大学》2016年硕士论文

【摘要】：缺失数据广泛存在于生命科学、农业、社会经济、环境科学等领域,但经典的统计数据研究中,大多是对完全数据进行统计分析,因此对缺失数据特别是不可忽略缺失数据的研究是非常必要的.混合线性模型是一般线性回归模型的推广与发展,其在研究分析重复观测数据(如面板数据、纵向数据)、分组数据以及空间数据时都具有明显的特有优势.混合线性模型不再受制于传统的线性模型中对响应变量的诸多假设(如独立性、方差齐性),并可以根据实际数据的特点,相对灵活地确定其协方差的结构.本文用贝叶斯的方法对包括协变量和响应变量存在不可忽略缺失的混合线性模型进行统计研究,运用Gibbs与Metropolis-Hastings抽样相结合的办法处理缺失数据与随机效应,从而得到模型参数的贝叶斯估计,并用三个模拟试验与一个实际例子验证方法的有效性.结果表明,该方法不仅适用于混合线性模型,也适用于广义混合线性模型.
[Abstract]:The missing data are widely used in the fields of life science, agriculture, social economy, environmental science and so on. But in the classical statistical data research, most of them are statistical analysis of complete data. Therefore, it is necessary to study the missing data, especially the missing data. Hybrid linear model is a generalization and development of general linear regression model. It has obvious advantages in the research and analysis of repeated observation data (such as panel data, longitudinal data, grouped data and spatial data). The mixed linear model is no longer subject to many assumptions about the response variables (such as independence and homogeneity of variance) in the traditional linear model, and the structure of the covariance can be determined flexibly according to the characteristics of the actual data. In this paper, Bayesian method is used to study the mixed linear model, which includes covariable and response variable. Gibbs and Metropolis-Hastings sampling are used to deal with the missing data and random effect. The Bayesian estimation of the model parameters is obtained, and the effectiveness of the method is verified by three simulation experiments and an actual example. The results show that this method is suitable not only for mixed linear model but also for generalized mixed linear model.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.8

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