政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/59434

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/59434

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政大機構典藏 > 理學院 > 應用數學系 > 學位論文 > Item 140.119/59434

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/59434

題名:	修正條件分配勝率矩陣時最佳參考點之選取方法 The best reference point method for the modification of the conditional distribution odds ratio matrices
作者:	郭俊佑
貢獻者:	姜志銘宋傳欽郭俊佑
關鍵詞:	勝率矩陣相容條件機率矩陣參考點 odds ratio matrix compatibility conditional probability matrix reference point
日期:	2012
上傳時間:	2013-09-02 16:46:19 (UTC+8)
摘要:	Chen(2010)提出如何用勝率函數來判斷給定的連續條件分配是否相容，以及相容時如何求對應的聯合分配。本研究提出，在二維有限的情形下，如何用勝率矩陣來判斷給定的條件機率矩陣是否相容，以及相容時如何求對應的聯合機率矩陣。又給定的條件機率矩陣不相容時，我們介紹了四種修改勝率矩陣的方法，同時在使用幾何平均法調整勝率矩陣的過程中，也發現選取最佳參考點以獲得最佳近似聯合機率矩陣之方法，並且給予理論證明。最後以模擬的方式發現，在修改勝率矩陣的四種方法中，以幾何平均法所得到的近似聯合機率矩陣，其條件機率矩陣最常接近所給定的條件機率矩陣。 Chen (2010) provides the representations of odds ratio function to examine the compatibility of conditional probability density functions and gives the corresponding joint probability density functions if they are compatible. In this research, we provide the representations of odds ratio matrix to examine the compatibility of two discrete conditional probability matrices and give the corresponding joint probability matrix if they are compatible. For incompatible situations, we offer four methods to revise odds ratio matrices to find near joint probability matrices so that their conditional probability matrices are not far from the two given ones. That is, we provide four methods so that the sums of error squares are small. For each method, the sum of error squares may depend on the same reference point of two odds ratio matrices. We first discover by example that only the geometric method out of these four methods has a pattern to get the best reference point so that the sum of error squares is smallest. We then prove this finding in general. In addition, through simulation results, the geometric method would provide the smallest sum of error squares most often among these four methods. Hence, we suggest using geometric method. Its strategy to find the best reference point is also given.
參考文獻:	Chen, Hua Yun. (2010) Compatibility of conditionally specified models. Statistics and Probability Letters, 80, 670-677. Ip, Edward H., Wang, Yuchung J. (2009) Canonical representation of conditionally specified multivariate discrete distributions. Journal of Multivariate Analysis,100, 1282-1290.
描述:	碩士國立政治大學應用數學系數學教學碩士在職專班 99972003 101
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0099972003
資料類型:	thesis
顯示於類別:	[應用數學系] 學位論文

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