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題名 對平滑直方圖的貝氏與準貝氏方法之比較
A comparison on Bayesian and quasi-Bayesian methods for Histogram Smoothing作者 彭志弘
Peng, Chih-Hung貢獻者 姜志銘
Jiang, Jhy-Ming
彭志弘
Peng, Chih-Hung關鍵詞 多項分配
平滑性
過濾後Dirichlet分配
multinomial distribution
smooth
filtered-variate Dirichlet distribution日期 2000 上傳時間 18-Apr-2016 16:31:52 (UTC+8) 摘要 針對具有多項分配(multinomial distribution)母體的類別資料，貝氏分析通常採取Dirichlet分配作為其先驗分配(prior distribution)，但在很多實際應用時，卻會遭遇困難；例如，當我們欲推估各年齡層佔總勞動力人口之比例時，母體除具多項分配外，其相鄰類別之比例亦相對接近；換言之，此時母體為具有平滑性(smooth)的多項分配，若依然採用Dirichlet分配作為其先驗分配，則會因為Dirichlet分配本身不具有平滑的特性，因而在做貝氏分析時會產生困擾。對這個難題Dickey and Jiang於1998年提出一個解決之道，他們的理論是對Dirichlet分配作適當之調整，將經過線性轉換後之Dirichlet分配稱為過濾後Dirichlet分配(filtered-variate Dirichlet distribution)，以過濾後Dirichlet分配作為調整後之先驗分配。對於Dickey and Jiang提出的方法，我們重新以蒙地卡羅法(Monte Carlo method)求出貝氏解，同時也嘗試以類似Makov and Smith (1977)和Smith and Makov (1978)對混合分配(mixture distribution)所用之準貝氏方法(quasi-Bayesian method)來逼近貝氏解。而本文將由電腦模擬的方式，探討貝氏方法與準貝氏方法之執行結果，並且考察準貝氏方法之收斂行為，對準貝氏方法的使用時機提出建議。 參考文獻 [1] Dickey, J. M., and Jiang, T. J.(1998),``Filtered-variate Prior Distribution for Histogram Smoothing," Journal of the American Statistical Association Vol.93,No.442,Theory and Methods,651-662. [2] Jiang, T. J., Kadane, J. B., and Dickey, J. M.(1992),"Computation of Carlson`s Multiple Hypergeometric Funtion R for Bayesian Application," Journal of Computational and Graphical Statistics,1,231-251. [3] Jiang, T. J., and Dickey, J. M.(1998),"Bayesian Approachese to Categorical Data with Informative Censoring,"To be published. [4] Carlson, B. C.(1977),"Special Funtion of Applied Mathematics," New York:Academic Press. [5] Wilks, S. S.(1962), Mathematical Statistics, New York:John Wiley. [6] Makov, U. E. and Smith, A. F. M.(1977),"A Quasi-Bayes Unsupervised Learning Procedure for Priors,"IEEE Trans. Inf. Thoery, IT-23, 761-764. [7] Smith, A. F. M and Makov, U. E.(1978)," A Quasi-Bayes Sequential Procedure for Mixtures,"J. R. Statist. Soc. B, 40, No1, 106-112. [8] Venter, J. H.(1966)"On Dvroetzky Stochastic Approximation," Ann. Math. Statist, 37, 1534-1544. [9] U. S. Bureau of the Census (1975), Historical Statistics in the United States. Part I, Washington, D. C. : U. S. Government Printing Office. [10] U. S. Bureau of the Census (1987), Statistical Abstract of the United States 1988 (108th ed.), Washington, D. C. : U. S. Government Printing Office. [11] Hoffman, M. S. (1987), The World Almanac and Book of Facts1987, New York: Pharos. [12] 行政院主計處編印,"中華民國•台灣地區人力資源統計月報",民國76年~民國88年. 描述 碩士
國立政治大學
應用數學系
87751001資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001742 資料類型 thesis dc.contributor.advisor 姜志銘 zh_TW dc.contributor.advisor Jiang, Jhy-Ming en_US dc.contributor.author (Authors) 彭志弘 zh_TW dc.contributor.author (Authors) Peng, Chih-Hung en_US dc.creator (作者) 彭志弘 zh_TW dc.creator (作者) Peng, Chih-Hung en_US dc.date (日期) 2000 en_US dc.date.accessioned 18-Apr-2016 16:31:52 (UTC+8) - dc.date.available 18-Apr-2016 16:31:52 (UTC+8) - dc.date.issued (上傳時間) 18-Apr-2016 16:31:52 (UTC+8) - dc.identifier (Other Identifiers) A2002001742 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85500 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 87751001 zh_TW dc.description.abstract (摘要) 針對具有多項分配(multinomial distribution)母體的類別資料，貝氏分析通常採取Dirichlet分配作為其先驗分配(prior distribution)，但在很多實際應用時，卻會遭遇困難；例如，當我們欲推估各年齡層佔總勞動力人口之比例時，母體除具多項分配外，其相鄰類別之比例亦相對接近；換言之，此時母體為具有平滑性(smooth)的多項分配，若依然採用Dirichlet分配作為其先驗分配，則會因為Dirichlet分配本身不具有平滑的特性，因而在做貝氏分析時會產生困擾。對這個難題Dickey and Jiang於1998年提出一個解決之道，他們的理論是對Dirichlet分配作適當之調整，將經過線性轉換後之Dirichlet分配稱為過濾後Dirichlet分配(filtered-variate Dirichlet distribution)，以過濾後Dirichlet分配作為調整後之先驗分配。對於Dickey and Jiang提出的方法，我們重新以蒙地卡羅法(Monte Carlo method)求出貝氏解，同時也嘗試以類似Makov and Smith (1977)和Smith and Makov (1978)對混合分配(mixture distribution)所用之準貝氏方法(quasi-Bayesian method)來逼近貝氏解。而本文將由電腦模擬的方式，探討貝氏方法與準貝氏方法之執行結果，並且考察準貝氏方法之收斂行為，對準貝氏方法的使用時機提出建議。 zh_TW dc.description.tableofcontents 封面頁 證明書 致謝詞 論文摘要 目錄 1. 簡介 2. 貝氏與準貝氏法 2.1 Dickey and Jiang的貝氏法 2.1.1 貝氏解 2.1.2 過濾後先驗分配 2.2 準貝氏法 2.2.1 準貝氏解 2.2.2 收斂性 3. 模擬探討 4. 實例應用 5. 結論 References zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001742 en_US dc.subject (關鍵詞) 多項分配 zh_TW dc.subject (關鍵詞) 平滑性 zh_TW dc.subject (關鍵詞) 過濾後Dirichlet分配 zh_TW dc.subject (關鍵詞) multinomial distribution en_US dc.subject (關鍵詞) smooth en_US dc.subject (關鍵詞) filtered-variate Dirichlet distribution en_US dc.title (題名) 對平滑直方圖的貝氏與準貝氏方法之比較 zh_TW dc.title (題名) A comparison on Bayesian and quasi-Bayesian methods for Histogram Smoothing en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Dickey, J. M., and Jiang, T. J.(1998),``Filtered-variate Prior Distribution for Histogram Smoothing," Journal of the American Statistical Association Vol.93,No.442,Theory and Methods,651-662. [2] Jiang, T. J., Kadane, J. B., and Dickey, J. M.(1992),"Computation of Carlson`s Multiple Hypergeometric Funtion R for Bayesian Application," Journal of Computational and Graphical Statistics,1,231-251. [3] Jiang, T. J., and Dickey, J. M.(1998),"Bayesian Approachese to Categorical Data with Informative Censoring,"To be published. [4] Carlson, B. C.(1977),"Special Funtion of Applied Mathematics," New York:Academic Press. [5] Wilks, S. S.(1962), Mathematical Statistics, New York:John Wiley. [6] Makov, U. E. and Smith, A. F. M.(1977),"A Quasi-Bayes Unsupervised Learning Procedure for Priors,"IEEE Trans. Inf. Thoery, IT-23, 761-764. [7] Smith, A. F. M and Makov, U. E.(1978)," A Quasi-Bayes Sequential Procedure for Mixtures,"J. R. Statist. Soc. B, 40, No1, 106-112. [8] Venter, J. H.(1966)"On Dvroetzky Stochastic Approximation," Ann. Math. Statist, 37, 1534-1544. [9] U. S. Bureau of the Census (1975), Historical Statistics in the United States. Part I, Washington, D. C. : U. S. Government Printing Office. [10] U. S. Bureau of the Census (1987), Statistical Abstract of the United States 1988 (108th ed.), Washington, D. C. : U. S. Government Printing Office. [11] Hoffman, M. S. (1987), The World Almanac and Book of Facts1987, New York: Pharos. [12] 行政院主計處編印,"中華民國•台灣地區人力資源統計月報",民國76年~民國88年. zh_TW
