dc.contributor.advisor | 宋傳欽<br>姜志銘 | zh_TW |
dc.contributor.advisor | Song, Chwan-Chin<br>Jiang, Jyh-Ming | en_US |
dc.contributor.author (Authors) | 涂沁如 | zh_TW |
dc.contributor.author (Authors) | Tu, Chin-Ju | en_US |
dc.creator (作者) | 涂沁如 | zh_TW |
dc.creator (作者) | Tu, Chin-Ju | en_US |
dc.date (日期) | 2018 | en_US |
dc.date.accessioned | 27-Jul-2018 12:18:18 (UTC+8) | - |
dc.date.available | 27-Jul-2018 12:18:18 (UTC+8) | - |
dc.date.issued (上傳時間) | 27-Jul-2018 12:18:18 (UTC+8) | - |
dc.identifier (Other Identifiers) | G1047510071 | en_US |
dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/118962 | - |
dc.description (描述) | 碩士 | zh_TW |
dc.description (描述) | 國立政治大學 | zh_TW |
dc.description (描述) | 應用數學系 | zh_TW |
dc.description (描述) | 104751007 | zh_TW |
dc.description.abstract (摘要) | 實務上,我們常需要建構母體的機率模型,然而當母體所涉及的隨機變數愈多,亦即維度愈高時,直接建構高維度之聯合分配的難度就越高,故我們可試著透過一組維度較低的條件分配來獲得聯合分配,而是否存在聯合分配滿足這一組條件分配,即為所謂的相容性問題。本文首先將二維條件分配的相容性問題跟馬可夫鏈的對應關係做詳細比較。我們發現,由於二維條件分配所對應的馬可夫鏈是非週期性的,因此,Arnold(1989)利用馬可夫鏈的理論,提出聯合分配唯一存在的充要條件,可做進一步化簡。給定二維條件分配,若不能找到共同的聯合分配則稱他們是不相容的;不相容的程度有各種衡量指標,而這些指標之間的關係也是值得我們研究的課題。在條件分配不相容情況下,我們先透過模擬數據的方式,對Arnold, Castillo, Sarabia (2002)及顧仲航 (2011)所提出的四種不相容測度值進行觀察,試圖進一步獲得有關他們之間關係的資訊。接著,在2x2的條件機率矩陣下,我們推導出四種不相容測度ϵ1、ϵ2、ϵ3、ϵ4以及對偶測度ϵ3*的計算公式,而且獲得2ϵ1=ϵ2=ϵ3=ϵ3*=ϵ4 的結果。最後,在2xJ的條件機率矩陣下,J>=2,我們推導出ϵ2 與ϵ3的計算公式,並且證明出ϵ2=ϵ3的關係;同時也在Ix2的條件機率矩陣下,I>=2,推出ϵ2=ϵ3*。 | zh_TW |
dc.description.abstract (摘要) | In practice, we may need to construct a joint distribution for a population. However, when the dimension of the random variables corresponding to the population is higher, it is often more difficult to find such a high dimensional joint distribution. Hence, we can obtain a set of lower dimensional conditional distributions first, and then use them to find their corresponding joint distribution. If there is a joint distribution matching this set of conditional distributions, we say this set of conditional distributions is compatible.First, we study the relationship between the compatibility and Markov chain. Since the Markov chain corresponding to two dimensional conditional distributions is aperiodic, we can further simplfy the necessary and sufficient condition of uniquness of a joint distribution given by Arnold(1989).The two dimensional conditional distributions are called incompatible if there is no common joint distribution for them. There are a few measures of degree of incompatibility in literature. Our aim is to study, through the simulations first, the relation among the four measures of degree of incompatibility given by Arnold, Castillo, Sarabia (2002) and Ku (2010). We derive the computational formulas for these four measures of degree of incompatibility ϵ1, ϵ2, ϵ3, ϵ4 and the duality measure ϵ3* under 2x2 conditional probability matrices and prove that 2ϵ1=ϵ2=ϵ3=ϵ3*=ϵ4. In addition, we derive the computational formulas for ϵ2 and ϵ3 and prove that ϵ2=ϵ3 under 2xJ conditional probability matrices, where J>=2. Finally, we also show that ϵ2=ϵ3* under Ix2 conditional probability matrices, where I>=2. | en_US |
dc.description.tableofcontents | 目錄致謝 i中文摘要 iiAbstract iii目錄 v表目錄 vii圖目錄 viii第一章 緒論 1第一節 研究動機與目的 1第二節 論文架構 2第二章 文獻探討 3第一節 條件分配相容性問題之回顧 3第二節 條件分配不相容程度之測量 7第三章 馬可夫鏈在條件分配相容性問題上之應用 10第一節 馬可夫鏈簡介 10第二節 馬可夫鏈與相容性問題之對應關係 12第四章 2x2 條件機率矩陣不相容測度之推導 15第一節 不相容測度ϵ3 與ϵ3 之推導 16第二節 不相容測度ϵ4 之推導 21第三節 不相容測度ϵ2 之推導 23第四節 不相容測度ϵ1 之推導 25第五章 條件機率矩陣不相容測度之進一步探討 27第一節 四種不相容測度之關係-實例觀察 27第二節 2x3 條件機率矩陣不相容測度之計算-實例說明 29第三節 2x3 條件機率矩陣不相容測度ϵ2 與ϵ3 之推導 33第六章 結論 38參考文獻 39表目錄4.1 2x2 條件機率矩陣下各測度值的相關結果 155.1 3x3 條件機率矩陣下各測度的相關結果 285.2 2x3 條件機率矩陣下測度二、三的相關結果 29圖目錄4.1 2x2 條件機率矩陣下ϵ3 之圖解法 175.1 2x3 條件機率矩陣下ϵ3 之圖解法 31 | zh_TW |
dc.format.extent | 939909 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G1047510071 | en_US |
dc.subject (關鍵詞) | 條件機率矩陣 | zh_TW |
dc.subject (關鍵詞) | 相容性 | zh_TW |
dc.subject (關鍵詞) | 馬可夫鏈 | zh_TW |
dc.subject (關鍵詞) | 不可約化 | zh_TW |
dc.subject (關鍵詞) | 不相容 | 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) | Markov chain | en_US |
dc.subject (關鍵詞) | Irreducible | en_US |
dc.subject (關鍵詞) | Incompatibility | en_US |
dc.title (題名) | 有限離散條件機率分布不相容測度之探討 | zh_TW |
dc.title (題名) | A study on the incompatibility of finite discrete conditional distributions | en_US |
dc.type (資料類型) | thesis | en_US |
dc.relation.reference (參考文獻) | 參考文獻Arnold, B. C., Castillo, E., and Sarabia, J. M. (2002). Exact and near compatibility of discrete conditional distributions. Comput. Stat. Data Anal., 40(2):231–252.Arnold, B. C. and Press, S. J. (1989). Compatible conditional distributions. Journal of the American Statistical Association, 84(405):152–156.Song, C.-C., Li, L.-A., Chen, C.-H., Jiang, T. J., and Kuo, K.-L. (2010). Compatibility of finite discrete conditional distributions. Statistica Sinica 20 (2010).Yates, R. and Goodman, D. (2005). Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers. John Wiley & Sons, second edition.黃文璋(1995). 隨機過程. 華泰文化事業股份有限公司.顧仲航(2011). 以特徵向量法解條件分配相容性問題. 國立政治大學應用數學系碩士論文. | zh_TW |
dc.identifier.doi (DOI) | 10.6814/THE.NCCU.MATH.005.2018.B01 | - |