【摘要】：列聯(lián)表是在醫(yī)學(xué)、工農(nóng)業(yè)、生物學(xué)以及社會(huì)科學(xué)中有著廣泛的應(yīng)用,隨著統(tǒng)計(jì)方法應(yīng)用范圍的擴(kuò)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(dú)立和有雙層混合先驗(yàn)分布的情況下各個(gè)細(xì)胞的Bayes估計(jì),得到了Bayes估計(jì)的準(zhǔn)確表達(dá)式以及兩個(gè)近似結(jié)果,是列聯(lián)表貝葉斯估計(jì)的推廣和改進(jìn),并且,進(jìn)行了實(shí)例驗(yàn)證,對(duì)比極大似然估計(jì),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(dú)立與圖模型聯(lián)系起來,為以后更高維和更復(fù)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(jì)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(gè)細(xì)胞參數(shù)的極大似然估計(jì)和Bayes估計(jì),以及在有混合先驗(yàn)時(shí)的Bayes估計(jì).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(yàn)時(shí)的Bayes估計(jì),得到了準(zhǔn)確表達(dá)式及兩個(gè)近似結(jié)果.第四章主要給出一個(gè)實(shí)例對(duì)第二章、第三章得出的結(jié)論進(jìn)行驗(yàn)證,從而使我們對(duì)有條件獨(dú)立的列聯(lián)表的Bayes估計(jì)有了新的認(rèn)識(shí)。
[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(xué)位授予單位】：湖北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：C815

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 姚宗靜;余強(qiáng);;Dirichlet分布概率密度的導(dǎo)出及若干性質(zhì)[J];科技信息;2010年11期

2 李開燦;有缺失數(shù)據(jù)的2×2×2列聯(lián)表的參數(shù)估計(jì)[J];數(shù)理統(tǒng)計(jì)與管理;2003年02期

3 李開燦,耿直;條件獨(dú)立性的三種形式及其相互關(guān)系[J];北京大學(xué)學(xué)報(bào)(自然科學(xué)版);2002年05期

4 方碧琪;Dirichlet先驗(yàn)的信息比[J];應(yīng)用數(shù)學(xué)學(xué)報(bào);1999年02期

5 趙博娟,吳喜之;形成過程不同的列聯(lián)表的檢驗(yàn)[J];數(shù)理統(tǒng)計(jì)與應(yīng)用概率;1997年02期

6 張堯庭;統(tǒng)計(jì)中的三大學(xué)派[J];統(tǒng)計(jì)教育;1995年01期

相關(guān)碩士學(xué)位論文 前1條

1 王鵬;定性資料與列聯(lián)表的統(tǒng)計(jì)分析[D];陜西師范大學(xué);2001年

，

本文編號(hào)：2274918