| dc.contributor.advisor | 宋傳欽 | zh_TW |
| dc.contributor.advisor | Song, Chwan Chin | en_US |
| dc.contributor.author (Authors) | 鄭鴻輝 | zh_TW |
| dc.contributor.author (Authors) | Jheng, Hong Huei | en_US |
| dc.creator (作者) | 鄭鴻輝 | zh_TW |
| dc.creator (作者) | Jheng, Hong Huei | en_US |
| dc.date (日期) | 2015 | en_US |
| dc.date.accessioned | 3-Aug-2015 13:31:03 (UTC+8) | - |
| dc.date.available | 3-Aug-2015 13:31:03 (UTC+8) | - |
| dc.date.issued (上傳時間) | 3-Aug-2015 13:31:03 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G1017510041 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/77243 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 101751004 | zh_TW |
| dc.description.abstract (摘要) | 給定聯合分配，可以容易地導出對應的條件分配。反之，給定條件分配的資訊，是否能導出對應的聯合分配呢？例如根據O. Paul et al.（1963，1968）對造成心血管疾病因素之追蹤研究，可得出咖啡量、吸菸量及是否有心血管疾病三者間的條件機率模型資料，是否能找到對應的聯合機率模型，以便可以更深入地研究三者之關係，是一個重要的議題。在選定參考點下，Chen（2010）提出以勝算比法找條件密度函數相容的充要條件，以及在相容性成立時，如何求得聯合分配。在二維中，當兩正值條件機率矩陣不相容時，郭俊佑（2013）以幾何平均法修正勝算比矩陣，並導出近似聯合分配，同時利用幾何平均法之特性，提出最佳參考點之選擇法則。本研究以二維的勝算比法為基礎，探討三維離散的相容性問題，獲得下列幾項結果：一、證明了三個三維條件機率矩陣相容的充要條件就是兩兩相容。二、當三維條件機率矩陣不相容時，利用幾何平均法導出近似聯合分配。三、利用兩兩相容的充要條件，導出三維條件機率矩陣相容的充要條件，並證明該充要條件與Chen的結果一致。四、在幾何平均法下，提出最少點法，有效率地找出最佳參考點，以產生總誤差最小的近似聯合分配。五、設計出程式檢驗三維條件機率矩陣是否相容，並找出最佳參考點，同時比較最少點法與窮舉法之間效率的差異。 | zh_TW |
| dc.description.abstract (摘要) | Given a joint distribution, we can easily derive the corresponding fully conditional distributions. Conversely, given fully conditional distributions, can we find out the corresponding joint distribution? For example, according to a longitudinal study of coronary heart disease risk factors by O. Paul et al. (1963, 1968), we obtain conditional probability model data among coffee intake, the number of cigarettes smoked and whether he/she has coronary heart disease or not. Whether we can find out the corresponding joint distribution is an important issue as the joint distribution may be used to do further analyses. Chen (2010) used odds ratio method to find a necessary and sufficient condition for their compatibility and also gave the corresponding joint distribution for compatible situations. When two positive discrete conditional distributions in two dimensions are incompatible, Kuo (2013) used a geometric mean method to modify odds ratio matrices and derived an approximate joint distribution. Kuo also provided a rule to find the best reference point when the geometric mean method is used. In this research, based on odds ratio method in two dimensions, we discuss their compatibility problems and obtain the following results on three-dimensional discrete cases. Firstly, we prove that a necessary and sufficient condition for the compatibility of three conditional probability matrices in three dimensions is pairwise compatible. Secondly, we extend Kuo’s method on two-dimensional cases to derive three-dimensional approximate joint distributions for incompatible situations. Thirdly, we derive a necessary and sufficient condition for the compatibility of three conditional probability matrices in three dimensions in terms of pairwise compatibility and also prove that this condition is consistent with Chen’s results. Fourthly, we provide a minimum-points method to efficiently find the best reference point and yield an approximate joint distribution such that total error is the smallest. Fifthly, we design a computer program to run three-dimensional discrete conditional probability matrices problems for compatibility and also compare the efficiency between minimum-points method and exhausting method. | en_US |
| dc.description.tableofcontents | 謝辭 iv中文摘要 vAbstract vi目次 viii表目次 xi1. 簡介 11.1 研究動機 11.2 研究目的 21.3 研究架構 32. 文獻回顧 42.1 二維中勝算比矩陣之介紹 42.2 二維中修正勝算比矩陣之方法 62.3 二維中最佳參考點之選擇 73. 三維條件機率矩陣相容性之檢驗 93.1 三維條件機率矩陣之介紹 93.2 Arnold-Press比值矩陣檢驗法 103.3 兩兩相容檢驗法 113.4 兩兩相容檢驗法在實例上的應用 134. 三維近似聯合分配 194.1 三維近似聯合分配之求法 194.2 模擬與實例探討 275. 三維中最佳參考點之求法 365.1 最少點法 365.2 尋找最少點集之方式 395.3 模擬與實例探討 455.4 最少點法與窮舉法之比較 486. 結論 49參考文獻 50附錄 附表 -1-附錄1：檢驗三維條件分配相容性程式etatest3.m之程式碼與操作方式 -1-附錄2：計算近似聯合分配程式geoajt.m之程式碼與操作方式 -4-附錄3：計算第一誤差程式geoe1.m之程式碼與操作方式 -7-附錄4：計算第二誤差程式geoe2.m之程式碼與操作方式 -9-附錄5：計算第三誤差程式geoe3.m之程式碼與操作方式 -11-附錄6：最少點法程式minpts.m之程式碼與操作方式 -13-附錄7：窮舉法程式exhpts.m之程式碼與操作方式 -17-附表1：大小為10x10x10的三維條件機率矩陣A -20-附表2：大小為10x20x20的三維條件機率矩陣B -23-附表3：大小為20x20x20的三維條件機率矩陣C -26-附表4：大小為10x10x10的三維條件機率矩陣A -29-附表5：大小為10x20x20的三維條件機率矩陣B -39-附表6：大小為20x20x20的三維條件機率矩陣C -49-附表7：大小為10x10x10的三維條件機率矩陣A -59-附表8：大小為10x20x20的三維條件機率矩陣B -79-附表9：大小為20x20x20的三維條件機率矩陣C -99- | zh_TW |
| dc.format.extent | 9620621 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G1017510041 | en_US |
| dc.subject (關鍵詞) | 條件機率矩陣 | zh_TW |
| dc.subject (關鍵詞) | 相容 | zh_TW |
| dc.subject (關鍵詞) | 勝算比 | zh_TW |
| dc.subject (關鍵詞) | 近似聯合分配 | zh_TW |
| dc.subject (關鍵詞) | 參考點 | zh_TW |
| dc.subject (關鍵詞) | 最少點法 | zh_TW |
| dc.subject (關鍵詞) | conditional probability matrix | en_US |
| dc.subject (關鍵詞) | compatibility | en_US |
| dc.subject (關鍵詞) | odds ratio | en_US |
| dc.subject (關鍵詞) | approximate joint distribution | en_US |
| dc.subject (關鍵詞) | reference point | en_US |
| dc.subject (關鍵詞) | minimum-points method | en_US |
| dc.title (題名) | 勝算比法在三維離散條件分配上的研究 | zh_TW |
| dc.title (題名) | Odds Ratio Method on Three-Dimensional Discrete Conditional Distributions | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | Arnold, Barry C. and Press, S. James (1989), ‘‘Compatible conditional distributions”, Journal of the American Statistical Association 84 (405), 152-156.Chen, Hua Yun (2010), “Compatibility of conditionally specified models”, Statistics and Probability Letters 80 (7-8), 670-677.Paul, O., Lepper, M. H., Phelan, W. H., Dupertius, G. W., MacMillan, A., McKean, H., and Park, H. (1963), “A longitudinal study of coronary heart disease”, Circulation 28 (20), 20-31.Paul, O., MacMillan, A., McKean, H., and Park, H. (1968), “Sucrose intake and coronary heart disease”, Lancet 2 (7577), 1049-1051.邓薇（2011），MATLAB函数速查手册（修订版），北京：人民邮电出版社。張智星（2000），MATLAB程式設計與應用，台北：清蔚科技。郭俊佑（2013），修正條件分配勝率矩陣時最佳參考點之選取方法，國立政治大學應用數學系碩士論文。 | zh_TW |
