带有混合先验的V-型图结构的Bayes估计
发布时间：2018-10-16 16:11
【摘要】：列联表是在医学、工农业、生物学以及社会科学中有着广泛的应用,随着统计方法应用范围的扩展和深入,日益受到重视.本文主要在列联表的基础上,探讨了I′J′K维列联表变量在存在条件独立和有双层混合先验分布的情况下各个细胞的Bayes估计,得到了Bayes估计的准确表达式以及两个近似结果,是列联表贝叶斯估计的推广和改进,并且,进行了实例验证,对比极大似然估计,发现结果是合理的;其次,本文引入了图的概念,将条件独立与图模型联系起来,为以后更高维和更复杂的研究奠定基础和指明方向.本文的安排如下:第一章为引言,简要介绍列联表、Bayes估计以及图模型的概念及发展,以及在这些方面的研究现状和本文的主要内容.第二章主要研究了一般三维列联表各个细胞参数的极大似然估计和Bayes估计,以及在有混合先验时的Bayes估计.第三章是本文的主要成果,主要研究了在三维变量具有V型图结构且有混合先验时的Bayes估计,得到了准确表达式及两个近似结果.第四章主要给出一个实例对第二章、第三章得出的结论进行验证,从而使我们对有条件独立的列联表的Bayes估计有了新的认识。
[Abstract]:The list is widely used in medicine, industry and agriculture, biology and social sciences. With the expansion and deepening of the application of statistical methods, more and more attention has been paid to it. In this paper, on the basis of the column table, the Bayes estimation of each cell in the presence of conditional independence and double mixed prior distribution of I'J'K dimensionality table variables is discussed. The exact expression and two approximate results of the Bayes estimation are obtained, which is the generalization and improvement of the Bayesian estimation of the column table. Furthermore, an example is given to verify that the result is reasonable by comparing the maximum likelihood estimation with the maximum likelihood estimation. In this paper, the concept of graph is introduced, and the conditional independence is associated with the graph model, which lays the foundation and points out the direction for the further research on higher and more complex dimension. The arrangement of this paper is as follows: the first chapter is the introduction, which briefly introduces the concept and development of column table, Bayes estimation and graph model, as well as the present research situation in these aspects and the main contents of this paper. In chapter 2, we mainly study the maximum likelihood estimation and Bayes estimation of each cell parameter in the general three-dimensional list, and the Bayes estimation in the case of mixed priori. The third chapter is the main achievement of this paper. We mainly study the Bayes estimator when the three-dimensional variables have V-shape graph structure and mixed priori. The exact expression and two approximate results are obtained. In chapter 4, an example is given to verify the conclusions of chapter 2 and chapter 3, which makes us have a new understanding of the Bayes estimation of conditional independent column tables.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C815
本文编号：2274918
[Abstract]:The list is widely used in medicine, industry and agriculture, biology and social sciences. With the expansion and deepening of the application of statistical methods, more and more attention has been paid to it. In this paper, on the basis of the column table, the Bayes estimation of each cell in the presence of conditional independence and double mixed prior distribution of I'J'K dimensionality table variables is discussed. The exact expression and two approximate results of the Bayes estimation are obtained, which is the generalization and improvement of the Bayesian estimation of the column table. Furthermore, an example is given to verify that the result is reasonable by comparing the maximum likelihood estimation with the maximum likelihood estimation. In this paper, the concept of graph is introduced, and the conditional independence is associated with the graph model, which lays the foundation and points out the direction for the further research on higher and more complex dimension. The arrangement of this paper is as follows: the first chapter is the introduction, which briefly introduces the concept and development of column table, Bayes estimation and graph model, as well as the present research situation in these aspects and the main contents of this paper. In chapter 2, we mainly study the maximum likelihood estimation and Bayes estimation of each cell parameter in the general three-dimensional list, and the Bayes estimation in the case of mixed priori. The third chapter is the main achievement of this paper. We mainly study the Bayes estimator when the three-dimensional variables have V-shape graph structure and mixed priori. The exact expression and two approximate results are obtained. In chapter 4, an example is given to verify the conclusions of chapter 2 and chapter 3, which makes us have a new understanding of the Bayes estimation of conditional independent column tables.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C815
【参考文献】
相关期刊论文 前6条
1 姚宗静;余强;;Dirichlet分布概率密度的导出及若干性质[J];科技信息;2010年11期
2 李开灿;有缺失数据的2×2×2列联表的参数估计[J];数理统计与管理;2003年02期
3 李开灿,耿直;条件独立性的三种形式及其相互关系[J];北京大学学报(自然科学版);2002年05期
4 方碧琪;Dirichlet先验的信息比[J];应用数学学报;1999年02期
5 赵博娟,吴喜之;形成过程不同的列联表的检验[J];数理统计与应用概率;1997年02期
6 张尧庭;统计中的三大学派[J];统计教育;1995年01期
相关硕士学位论文 前1条
1 王鹏;定性资料与列联表的统计分析[D];陕西师范大学;2001年
，本文编号：2274918
本文链接：https://www.wllwen.com/shekelunwen/shgj/2274918.html
教材专著
