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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/54046


    Title: 隨機函數分配
    Other Titles: On the Random Functional Distributions
    Authors: 姜志銘
    Contributors: 國立政治大學應用數學學系
    行政院國家科學委員會
    Keywords: 貝氏無母數;Ferguson-Dirichlet過程;隨機函數;C-特徵函數
    Bayesian nonparametric;Ferguson-Dirichlet process;random functional;c-characteristic function
    Date: 2009
    Issue Date: 2012-10-24 16:13:51 (UTC+8)
    Abstract: 在貝氏統計領域內，最常用於隨機分配的無母數模型就是Ferguson-Dirichlet過程，我們首先將研究Ferguson-Dirichlet隨機過程的母數測度在球體內部，橢圓球表面，橢圓球內部的隨機函數分配。過濾變量Dirichlet分配的擴充就是Ferguson-Dirichlet隨機過程的隨機均值分配，為從另一角度研究隨機函數分配以及過濾變量Dirichlet分配的進一步應用，我們將研究及提供過濾變量Dirichlet分配和C-特徵函數的相關性質及結果。最後，我們將提供對Ferguson-Dirichlet隨機過程應用簡單及有效的數值計算方法。
    The Ferguson-Dirichlet process is the most widely used nonparametric model for random distributions in Bayesian statistics. We first study the distributions of the random functional of the Ferguson-Dirichlet process with parameter measure over spherical solid, ellipsoidal surface, and ellipsoidal solid. The generalization of the filtered-variate Dirichlet distribution is the distribution of a random mean of a Ferguson-Dirichlet process. To study the random functional from another point of views and further applications of the filter-variate Dirichlet distribution, we will also study and provide the related properties and results of the filtered-variate Dirichlet distributions and c-characteristic functions. Finally, we shall give easy and efficient computational methods for the Ferguson-Dirichlet process applications.
    Relation: 基礎研究
    學術補助
    研究期間:9808~ 9907
    研究經費:460仟元
    Data Type: report
    Appears in Collections:[應用數學系] 國科會研究計畫

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