标题： beta过程的构造性定义 显示英文标题

标题： A constructive definition of the beta process

摘要： 我们推导出一种贝塔过程的构造方法，该方法允许具有显著度量的原子首先被抽取。 我们的表示基于对 Sethuraman（1994）提出的狄利克雷过程构造的扩展，因此我们将它称为割棒构造。 我们的第一个证明使用了有限数组的极限情况论证。 为此，我们提出了一个有限筛逼近的贝塔过程，类似于 Ishwaran 和 Zarepour（2002）的方法，并证明了其收敛到贝塔过程。 我们给出了第二种利用泊松过程工具来构造的证明。 我们使用泊松过程推导出构造的几乎确定截断界。 最后，我们通过提出贝塔-伯努利和贝塔-负二项过程模型的有效采样算法来结束本文。 显示英文摘要

摘要： We derive a construction of the beta process that allows for the atoms with significant measure to be drawn first. Our representation is based on an extension of the Sethuraman (1994) construction of the Dirichlet process, and therefore we refer to it as a stick-breaking construction. Our first proof uses a limiting case argument of finite arrays. To this end, we present a finite sieve approximation to the beta process that parallels that of Ishwaran & Zarepour (2002) and prove its convergence to the beta process. We give a second proof of the construction using Poisson process machinery. We use the Poisson process to derive almost sure truncation bounds for the construction. We conclude the paper by presenting an efficient sampling algorithm for beta-Bernoulli and beta-negative binomial process models.