Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages
Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages
复制标题
贝叶斯泊松过程分区演算及其在贝叶斯 Lévy 移动平均线中的应用
DOI：
10.1214/009053605000000336
复制
发表时间：
2005
影响因子：
4.5
通讯作者：
Lancelot F. James
中科院分区：
文献类型：
--
作者：
Lancelot F. James
本文发展并描述了如何使用关于泊松随机测度分解的结果。这些结果被塑造成简单的工具，可以量身定做，以解决在广泛的贝叶斯非参数和空间统计模型中出现的推理问题。Poisson分解方法是基于两个结果的形式陈述，这两个结果是关于Laplace泛函测度变化和Poisson Palm/Fubini演算关于整数(1，…，n)的随机划分。这些技术类似于Dirichlet过程和加权Gamma过程的技术，但比{AN.统计学家。12(1984)351-3571和[Ann.安装统计学家。数学课。41(1989)227-245]。为了说明该方法的灵活性，给出了一大类随机概率测度和可表示为Poisson随机测度泛函的随机危险或强度。我们描述了离散随机概率类的统一后验分析，它识别并利用了所有这些模型的共同特征。该分析绕过了贝叶斯非参数演算中涉及的许多困难问题，包括组合分量。这使得人们可以专注于通过实值函数h表征的每个过程的独特特征。通过在乘性强度模型的一般设置下获得Levy-Cox移动平均过程的显式后验表达式，进一步说明了该技术的适用性。此外，对于这些模型，还简要讨论了与Dirichlet过程类似的新的计算方法。
This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address inferential questions arising in a wide range of Bayesian nonparametric and spatial statistical models. The Poisson disintegration method is based on the formal statement of two results concerning a Laplace functional change of measure and a Poisson Palm/Fubini calculus in terms of random partitions of the integers (1,...,n). The techniques are analogous to, but much more general than, techniques for the Dirichlet process and weighted gamma process developed in {Ann. Statist. 12 (1984) 351-3571 and [Ann. Inst. Statist. Math. 41 (1989) 227-245]. In order to illustrate the flexibility of the approach, large classes of random probability measures and random hazards or intensities which can be expressed as functionals of Poisson random measures are described. We describe a unified posterior analysis of classes of discrete random probability which identifies and exploits features common to all these models. The analysis circumvents many of the difficult issues involved in Bayesian nonparametric calculus, including a combinatorial component. This allows one to focus on the unique features of each process which are characterized via real valued functions h. The applicability of the technique is further illustrated by obtaining explicit posterior expressions for Levy-Cox moving average processes within the general setting of multiplicative intensity models. In addition, novel computational procedures, similar to efficient procedures developed for the Dirichlet process, are briefly discussed for these models.