The stick-breaking representation is one of the fundamental properties of the Dirichlet process. It represents the random probability measure as a discrete random sum whose weights and atoms are formed by independent and identically distributed sequences of beta variates and draws from the normalized base measure of the Dirichlet process parameter. It is used extensively in posterior simulation for statistical models with Dirichlet processes. The original proof of Sethuraman (Stat Sin 4:639–650, 1994) relies on an indirect distributional equation and does not encourage an intuitive understanding of the property. In this paper, we give a new proof of the stick-breaking representation of the Dirichlet process that provides an intuitive understanding of the theorem. The proof is based on the posterior distribution and self-similarity properties of the Dirichlet process.

中文翻译：

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Dirichlet过程的突破性表示的新证明

不折不扣的表现形式是狄利克雷过程的基本特性之一。它表示随机概率度量为离散的随机总和，其权重和原子由独立且相同分布的β变量序列形成，并取自Dirichlet过程参数的归一化基本度量。它广泛用于具有Dirichlet过程的统计模型的后验模拟中。Sethuraman的原始证明（Stat Sin 4：639–650，1994）依赖于间接分配方程，并不鼓励人们对财产有直观的了解。在本文中，我们提供了狄利克雷过程的突破性表示的新证明，该证明提供了对定理的直观理解。