隨機函數分配

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.