A moment-matching Ferguson & Klass algorithm

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• 作者：Julyan Arbel ; Igor Prünster
• 关键词：Bayesian Nonparametrics ; Completely random measures ; Ferguson & Klass algorithm ; Moment ; matching ; Normalized random measures ; Posterior sampling
• 刊名：Statistics and Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：3-17
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science;
• 出版者：Springer US
• ISSN：1573-1375
• 卷排序：27

文摘

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.