狄里克雷過程和中國餐廳程序

Abstract

在貝氏無母數統計學的領域中狄里克雷過程(DP)扮演非常重要的角色。狄里克雷過程(DP)是一群分布函數的集合。我們將討論一些和狄里克雷過程(DP)有關的定理和性質及一些建立在決策論(decision theory)上對於由狄里克雷過程(DP)抽出樣本的估計量。中國餐廳程序(CRP)也是一個隨機過程。由中國餐廳程序抽出的樣本是正整數的一個分割。我們使用不同的觀點去描述中國餐廳程序(CRP)。此外我們將討論狄里克雷過程(DP)和中國餐廳程序(CRP)之間的關係。

Dirichlet process (DP) plays an important role in Bayesian nonparametric statistics. Dirichlet process (DP) is a class of distributions. We discuss some theorems and related properties of DP. And we discuss estimations of a sample from DP base on decision theory. Chinese restaurant process (CRP) is also a stochastic process. The sample of CRP is a partition of positive integers. We use different viewpoints to describe Chinese restaurant process (CRP). Besides, we discuss the relationship of Dirichlet process (DP) and Chinese restaurant process (CRP).