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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/77916
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/77916


    Title: 離散條件機率分配之相容性研究
    On compatibility of discrete conditional distributions
    Authors: 陳世傑
    Chen, Shih Chieh
    Contributors: 姚怡慶
    Yao, Yi Ching
    陳世傑
    Chen, Shih Chieh
    Keywords: 條件機率分配之相容性
    圖論
    相連性
    展開樹
    吉布斯抽樣法
    蒙地卡羅馬可夫鏈法
    compatibility of conditional distributions
    graph theory
    connectedness
    spanning tree
    Gibbs sampler
    MCMC
    Date: 2015
    Issue Date: 2015-08-24 10:33:32 (UTC+8)
    Abstract: 設二個隨機變數X1 和X2,所可能的發生值分別為{1,…,I}和{1,…,J}。條件機率分配模型為二個I × J 的矩陣A 和B,分別代表在X2 給定的條件下X1的條件機率分配和在X1 給定的條件下X2的條件機率分配。若存在一個聯合機率分配,而且它的二個條件機率分配剛好就是A 和B,則稱A和B相容。我們透過圖形表示法,提出新的二個離散條件機率分配會相容的充分必要條件。另外,我們證明,二個相容的條件機率分配會有唯一的聯合機率分配的充分必要條件為:所對應的圖形是相連的。我們也討論馬可夫鏈與相容性的關係。
    For two discrete random variables X1 and X2 taking values in {1,…,I} and {1,…,J}, respectively, a putative conditional model for the joint distribution of X1 and X2 consists of two I × J matrices representing the conditional distributions of X1 given X2 and of X2 given X1. We say that two conditional distributions (matrices) A and B are compatible if there exists a joint distribution of X1 and X2 whose two conditional distributions are exactly A and B. We present new versions of necessary and sufficient conditions for compatibility of discrete conditional distributions via a graphical representation. Moreover, we show that there is a unique joint distribution for two given compatible conditional distributions if and only if the corresponding graph is connected. Markov chain characterizations are also presented.
    Reference: [1]Arnold, B. C. and Press, S. J. (1989). Campatible conditional distributions. Journal of the American Statistical Association ,84, 152-156.
    [2]Arnold, B. C. and Gokhale, D. V. (1998). Distributions most nearly compatible with given families of conditional distributions. Test 7 , 377-390.
    [3]Arnold, B. C., Castillo, E., and Sarbia, J. M. (1999). Conditional specification of statistical models. Springer, New York.
    [4]Arnold, B. C., Castillo, E., and Sarbia, J. M. (2001). Conditionally specified distribution: an introduction (with discussions). Statistical Science, 16, 249-274.
    [5]Arnold, B. C., Castillo, E., and Sarbia, J. M. (2002). Exact and near compatibility of discrete distributions. Computational Statistics and Data Analysis, 40, 231-252.
    [6]Arnold, B. C., Castillo, E., and Sarbia, J. M. (2004). Compatibility of partial or complete conditional probability specifications. Journal of Statistical Planning and Inference, 123, 133-159.
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    [12]Kuo, K-L, Wang, Y. J. (2011) A simple algorithm for checking compatibility among discrete conditional distributions. Computational Statistics and Data Analysis, 5, 2457-2462.
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    role of UGT1A1*28 polymorphism in the pharmacodynamics and pharmacokinetics of irinotecan in patients with metastatic colorectal cancer. Jounal of Clinical Oncology 24, 3061-3068.
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    [19]Yao, Y. C., Chen, S. C.,Wang, S. H. (2014). On compatibility of discrete full conditional distributions:A graphical representation approach. Journal of Multivariate Analysis,124, 1-9.
    Description: 博士
    國立政治大學
    統計研究所
    94354504
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0094354504
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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