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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 Chingen_US
dc.contributor.author (Authors) 陳世傑zh_TW
dc.contributor.author (Authors) Chen, Shih Chiehen_US
dc.creator (作者) 陳世傑zh_TW
dc.creator (作者) Chen, Shih Chiehen_US
dc.date (日期) 2015en_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) G0094354504en_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) 94354504zh_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 .......................... 7

3 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 ............................. 26

4 Markov chain characterizations 31
4.1 Compatibility by the Gibbs sampler ... 31
4.2 Simulations .......................... 49

5 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/#G0094354504en_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 distributionsen_US
dc.subject (關鍵詞) graph theoryen_US
dc.subject (關鍵詞) connectednessen_US
dc.subject (關鍵詞) spanning treeen_US
dc.subject (關鍵詞) Gibbs sampleren_US
dc.subject (關鍵詞) MCMCen_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 distributionsen_US
dc.type (資料類型) thesisen
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