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A moment-matching Ferguson & Klass algorithm

机译：矩匹配Ferguson＆Klass算法

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摘要

Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. The popular Ferguson & Klass representation of CRMs as a random series with decreasing jumps can immediately be turned into an algorithm for sampling realizations of CRMs or more elaborate models involving transformed CRMs. However, concrete implementation requires to truncate the random series at some threshold resulting in an approximation error. The goal of this paper is to quantify the quality of the approximation by a moment-matching criterion, which consists in evaluating a measure of discrepancy between actual moments and moments based on the simulation output. Seen as a function of the truncation level, the methodology can be used to determine the truncation level needed to reach a certain level of precision. The resulting moment-matching Ferguson & Klass algorithm is then implemented and illustrated on several popular Bayesian nonparametric models.
机译：完全随机测度（CRM）代表了各种流行随机模型的关键组成部分，并且在现代贝叶斯非参数学中起着举足轻重的作用。流行的Ferguson＆Klass CRM表示为具有减少的跳变的随机序列，可以立即转变为用于对CRM的实现采样或涉及转换CRM的更精细模型的算法。但是，具体实现需要在某个阈值处截断随机序列，从而导致近似误差。本文的目的是通过一个矩匹配标准来量化近似值的质量，该准则包括根据模拟输出评估实际矩与矩之间的差异的度量。被视为截断水平的函数，该方法可用于确定达到一定精度水平所需的截断水平。然后在几种流行的贝叶斯非参数模型上实现并说明了所得的矩匹配Ferguson＆Klass算法。

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