政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/77916
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 113318/144297 (79%)
Visitors : 51075385      Online Users : 940
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
    •  Adv. Search
    Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer Goto mobile version


    Please use this identifier to cite or link to this item: https://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.
    [7]Besag , J., (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B 36, 192-236.
    [8]Gelman, A. and Speed, T. P. (1993). Characterizing a joint probability distribution by conditionals. Journal of the Royal Statistical Society. Series B 55, 185-188.
    [9]Gourieroux, C. and Monfort, A. (1979). On the characterization of a joint probability distribution by conditional distributions. Journal of Econometrics, 10, 115-118.
    [10]Hobert, J. P. and Casella, G. (1998) Functional compatibility, markov chains, and Gibbs sampling with improper posteriors. Journal of Computational and Graphical Statistics, 7, 42-60.
    [11]Ip, E. H., Wang, Y. J., (2009) Canonical representation of conditionally specified multivariate discrete distributions. Journal of Multivariate Analysis, 100, 1282-1290 .
    [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.
    [13]Liu, J. S. (1996) Discussion of “Statistical inference and Monte Carlo algorithms” by Casella, G. Test 5, 305-310.
    [14]Slavkovic, A. B., Sullivant, S., (2006) The space of compatible full conditionals is a unimodular toric variety. Journal of Symbolic Computation, 41, 196-209.
    [15]Song, C. C., Li, L. A., Chen, C. H., Jiang, T. J. and Kuo, K. L. (2010). Compatibilty of finie discrete conditional distributions. Statistica Sinica, 20, 423-440.
    [16]Tian, G. L., Tan, M., Ng, K. W. and Tang, M. L. (2009). A unified method for checking compatibility and uniqueness for finite discrete conditional distributions.
    Communications in Statistics-Theory and Models, 38, 115-129.
    [17] Toffoli, E., Cecchin, E., Corona, G., Russo, A., Buonadonna, A., D’Andrea, M., Pasetto, L., Pessa, S., Errante, D., De Pangher, V., Giusto, M., Medici, M., Gaion, F., Sandri, P., Galligioni, E., Bonura, S., Boccalon, M., Biason, P., Frustaci, S. (2006). The
    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.
    [18]Wang, Y. J., Kuo, K-L. (2010) Compatibility of discrete conditional distributions with structural zeros. Journal of Multivariate Analysis,101, 191-199.
    [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:[Department of Statistics] Theses

    Files in This Item:

    File SizeFormat
    450401.pdf633KbAdobe PDF2130View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback