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題名 以比值矩陣法處理高維度中相容性問題
其他題名 Solving the Compatibility Issue in Higher Dimensions with Ratio Matrix Method
作者 宋傳欽
貢獻者 國立政治大學應用數學學系
行政院國家科學委員會
關鍵詞 相容性;IBD比值矩陣;完全條件分配函數
compatibility;IBD ratio matrix;full conditional densities
日期 2009
上傳時間 24-Oct-2012 16:13:54 (UTC+8)
摘要 在給定一些條件分配函數時，若存在聯合分配函數使得其條件分配函數跟給定的條件分配函數相同時，則稱這些給定的條件分配函數是相容的。二維有限離散型相容性問題由Arnold et al.（1989）率先提出以比值矩陣（ratio matrix）作為解決問題的核心工具。Song et al.（2008）延續相關的研究，並提出了IBD比值矩陣（irreducible block diagonal ratio matrix）的突破性概念，給予了是否相容？以及相容時，聯合機率分配是否唯一的簡單、方便、快速檢驗方法。同時，當聯合機率分配函數解不唯一時，Song et al.（2008）也給予了找出所有可能解的方法。本計畫擬將前述二維有限離散的結果推廣至高維度的情形，即給定一些多個隨機變數的完全條件分配函數（full conditional distributions），如何運用相關的比值矩陣，判斷他們是相容的？若相容時，又如何找出所有聯合分配函數的解？
The given conditional densities are said to be compatible if there exists an associated joint density with them as its conditionals. Arnold et al.（1989）first used the ratio matrix to solve for the bivariate case. However, there is some insufficiency in their main theorem. Song et al.（2008）proposed the IBD ratio matrix concept, and gave a simple and easy manipulation method for compatibility checking and uniqueness checking. Besides, they also gave a way to find all possible joint densities whenever the solutions are not unique. In this study, we will extend the results obtained in bivariate case to those in high-dimensional cases for full conditional densities.
關聯 基礎研究
學術補助
研究期間:9808~ 9907
研究經費:326仟元
資料類型 report
dc.contributor 國立政治大學應用數學學系en_US
dc.contributor 行政院國家科學委員會en_US
dc.creator (作者) 宋傳欽zh_TW
dc.date (日期) 2009en_US
dc.date.accessioned 24-Oct-2012 16:13:54 (UTC+8)-
dc.date.available 24-Oct-2012 16:13:54 (UTC+8)-
dc.date.issued (上傳時間) 24-Oct-2012 16:13:54 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54048-
dc.description.abstract (摘要) 在給定一些條件分配函數時，若存在聯合分配函數使得其條件分配函數跟給定的條件分配函數相同時，則稱這些給定的條件分配函數是相容的。二維有限離散型相容性問題由Arnold et al.（1989）率先提出以比值矩陣（ratio matrix）作為解決問題的核心工具。Song et al.（2008）延續相關的研究，並提出了IBD比值矩陣（irreducible block diagonal ratio matrix）的突破性概念，給予了是否相容？以及相容時，聯合機率分配是否唯一的簡單、方便、快速檢驗方法。同時，當聯合機率分配函數解不唯一時，Song et al.（2008）也給予了找出所有可能解的方法。本計畫擬將前述二維有限離散的結果推廣至高維度的情形，即給定一些多個隨機變數的完全條件分配函數（full conditional distributions），如何運用相關的比值矩陣，判斷他們是相容的？若相容時，又如何找出所有聯合分配函數的解？en_US
dc.description.abstract (摘要) The given conditional densities are said to be compatible if there exists an associated joint density with them as its conditionals. Arnold et al.（1989）first used the ratio matrix to solve for the bivariate case. However, there is some insufficiency in their main theorem. Song et al.（2008）proposed the IBD ratio matrix concept, and gave a simple and easy manipulation method for compatibility checking and uniqueness checking. Besides, they also gave a way to find all possible joint densities whenever the solutions are not unique. In this study, we will extend the results obtained in bivariate case to those in high-dimensional cases for full conditional densities.en_US
dc.language.iso en_US-
dc.relation (關聯) 基礎研究en_US
dc.relation (關聯) 學術補助en_US
dc.relation (關聯) 研究期間:9808~ 9907en_US
dc.relation (關聯) 研究經費:326仟元en_US
dc.subject (關鍵詞) 相容性;IBD比值矩陣;完全條件分配函數en_US
dc.subject (關鍵詞) compatibility;IBD ratio matrix;full conditional densitiesen_US
dc.title (題名) 以比值矩陣法處理高維度中相容性問題zh_TW
dc.title.alternative (其他題名) Solving the Compatibility Issue in Higher Dimensions with Ratio Matrix Methoden_US
dc.type (資料類型) reporten