發(fā)布時間：2018-10-16 16:11

【摘要】：列聯(lián)表是在醫(yī)學、工農(nóng)業(yè)、生物學以及社會科學中有著廣泛的應用,隨著統(tǒng)計方法應用范圍的擴展和深入,日益受到重視.本文主要在列聯(lián)表的基礎(chǔ)上,探討了I′J′K維列聯(lián)表變量在存在條件獨立和有雙層混合先驗分布的情況下各個細胞的Bayes估計,得到了Bayes估計的準確表達式以及兩個近似結(jié)果,是列聯(lián)表貝葉斯估計的推廣和改進,并且,進行了實例驗證,對比極大似然估計,發(fā)現(xiàn)結(jié)果是合理的;其次,本文引入了圖的概念,將條件獨立與圖模型聯(lián)系起來,為以后更高維和更復雜的研究奠定基礎(chǔ)和指明方向.本文的安排如下:第一章為引言,簡要介紹列聯(lián)表、Bayes估計以及圖模型的概念及發(fā)展,以及在這些方面的研究現(xiàn)狀和本文的主要內(nèi)容.第二章主要研究了一般三維列聯(lián)表各個細胞參數(shù)的極大似然估計和Bayes估計,以及在有混合先驗時的Bayes估計.第三章是本文的主要成果,主要研究了在三維變量具有V型圖結(jié)構(gòu)且有混合先驗時的Bayes估計,得到了準確表達式及兩個近似結(jié)果.第四章主要給出一個實例對第二章、第三章得出的結(jié)論進行驗證,從而使我們對有條件獨立的列聯(lián)表的Bayes估計有了新的認識。
[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.
【學位授予單位】：湖北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：C815

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本文編號：2274918