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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/49462


    Title: von Mises-Fisher分配資料的半母數貝氏分析法
    Semi-parametric Bayesian analysis on von Mises-Fisher distribution data
    Authors: 林其緯
    Lin,Chi Wei
    Contributors: 姜志銘
    林其緯
    Lin,Chi Wei
    Keywords: Dirichlet過程
    von Mises-Fisher分配
    半母數貝氏分析法
    Date: 2009
    Issue Date: 2010-12-08 11:54:34 (UTC+8)
    Abstract: 在許多科學領域裡所蒐集到的資料是具有方向性且落在單位球上，而在具有方向性且在單位球上的資料分配中，最重要也是最常使用的分配是3維的von Mises-Fisher分配。在過去有許多學者專家曾分析過具有3維von Mises-Fisher分配的資料，其中Nunez-Antonio和Gutierrez-Pena (2005)也曾利用全貝氏法來分析此種資料。本文首次嘗試利用半母數貝氏法來分析具有3維von Mises-Fisher分配的資料。除了介紹如何估計參數以及預測未來資料的機率密度函數外，本文也將檢定兩組分別服從不同3維von Mises-Fisher分配的資料其平均方向是否相同，並且提供選取先驗分配與其參數之建議。
    Reference: 1. Antoniak, C. E. (1974). Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems,
    The Annals of Statistics, 2, 1152-1174.
    2. Blackwell, D., and MacQueen, J.B. (1973). Ferguson Distribution via Polya Urn Schemes, The Annals of Statistics, 1, 353-355.
    3. Escobar, M. D. (1994). Estimating Normal Means with a Dirichlet Process Prior,
    Journal of the American Statistical Association, 89, 268-277.
    4. Escobar, M. D. (1995). Nonparametric Bayesian Methods in Hierarchical Models, Journal of Statistical Planning and Inference, 43, 97-106.
    5. Ferguson, T. S. (1973). A Bayesian Analysis of Some Nonparametric Problems, The Annals of Statistics, 1, 209-230.
    6. Fisher, N.I., Lewis, T., and Embleton, B.J.J. (1987). Statistical Analysis of Spherical Data, Combridge: university Press.
    7. Gelfand, A. E., and Smith, A. F. M. (1990). Sampling-Based Approaches to Calculating Marginal Densities,
    Journal of the American Statistical Association, 85, 398-409.
    8. Ghosh, K., Jammalamadaka, S. R., and Tiwari, R. C. (2003). Semiparametric Bayesian Techniques for Problems in Circular Data, Journal of Applied Statistics, 30, 145-161.
    9. Jammalamadaka, S. R.,and SenGupta, A. (2001). Topics in Circular Statistics, Singapore: World Scientific.
    10. Mardia, K. V. (1972) Statistics od Directional Data, London: Academic Press.
    11. Mardia, K. V. and Jupp, P. E. (2000) Directional Statistics, Chichester: John Wiley and Sons, Ltd.
    12. Nunez-Antonio, G. and Gutierrez-Pena, E. (2005). A Bayesian Analysis of Directional Data Using the von Mises-Fisher Distribution, Communications in Statistics-Simulation and Computation, 34, 989-999.
    13. Press, S. J. (2003) Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, John Wiley and Sons, New Jersey.
    Description: 碩士
    國立政治大學
    應用數學研究所
    92751007
    98
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0927510071
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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