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題名 離散條件機率分配之相容性研究
On compatibility of discrete conditional distributions作者 陳世傑
Chen, Shih Chieh貢獻者 姚怡慶
Yao, Yi Ching
陳世傑
Chen, Shih Chieh關鍵詞 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日期 2015 上傳時間 24-Aug-2015 10:33:32 (UTC+8) 摘要 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.參考文獻 [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. 描述 博士
國立政治大學
統計研究所
94354504資料來源 http://thesis.lib.nccu.edu.tw/record/#G0094354504 資料類型 thesis dc.contributor.advisor 姚怡慶 zh_TW dc.contributor.advisor Yao, Yi Ching en_US dc.contributor.author (Authors) 陳世傑 zh_TW dc.contributor.author (Authors) Chen, Shih Chieh en_US dc.creator (作者) 陳世傑 zh_TW dc.creator (作者) Chen, Shih Chieh en_US dc.date (日期) 2015 en_US dc.date.accessioned 24-Aug-2015 10:33:32 (UTC+8) - dc.date.available 24-Aug-2015 10:33:32 (UTC+8) - dc.date.issued (上傳時間) 24-Aug-2015 10:33:32 (UTC+8) - dc.identifier (Other Identifiers) G0094354504 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/77916 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 94354504 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 1 Introduction 1 2 Compatible conditional distributions 5 2.1 Compatibility ......................... 5 2.2 Review of the ratio matrix approach for compatibility between two conditional distribution .......................... 73 Graphical representation approach 14 3.1 Graphical representation ............. 14 3.2 Compatibility of a ratio set R and characterization of probability distributions satisfying R ........... 19 3.3 The relation between the ratio matrix approach and graphical representation approach ............................. 264 Markov chain characterizations 31 4.1 Compatibility by the Gibbs sampler ... 31 4.2 Simulations .......................... 495 Conclusions 55 References 57 zh_TW dc.format.extent 648347 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094354504 en_US dc.subject (關鍵詞) 條件機率分配之相容性 zh_TW dc.subject (關鍵詞) 圖論 zh_TW dc.subject (關鍵詞) 相連性 zh_TW dc.subject (關鍵詞) 展開樹 zh_TW dc.subject (關鍵詞) 吉布斯抽樣法 zh_TW dc.subject (關鍵詞) 蒙地卡羅馬可夫鏈法 zh_TW dc.subject (關鍵詞) compatibility of conditional distributions en_US dc.subject (關鍵詞) graph theory en_US dc.subject (關鍵詞) connectedness en_US dc.subject (關鍵詞) spanning tree en_US dc.subject (關鍵詞) Gibbs sampler en_US dc.subject (關鍵詞) MCMC en_US dc.title (題名) 離散條件機率分配之相容性研究 zh_TW dc.title (題名) On compatibility of discrete conditional distributions en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [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. zh_TW
