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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/85500


    Title: 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
    Authors: 彭志弘
    Peng, Chih-Hung
    Contributors: 姜志銘
    Jiang, Jhy-Ming
    彭志弘
    Peng, Chih-Hung
    Keywords: 多項分配
    平滑性
    過濾後Dirichlet分配
    multinomial distribution
    smooth
    filtered-variate Dirichlet distribution
    Date: 2000
    Issue Date: 2016-04-18 16:31:52 (UTC+8)
    Abstract: 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。
    Reference: [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.
    Description: 碩士
    國立政治大學
    應用數學系
    87751001
    Source URI: http://thesis.lib.nccu.edu.tw/record/#A2002001742
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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