Abstract

We consider modeling a dependent sequence of random partitions. It is well known in Bayesian nonparametrics that a random measure of discrete type induces a distribution over random partitions. The community has therefore assumed that the best approach to obtain a dependent sequence of random partitions is through modeling dependent random measures. We argue that this approach is problematic and show that the random partition model induced by dependent Bayesian nonparametric priors exhibits counter-intuitive dependence among partitions even though the dependence for the sequence of random probability measures is intuitive. Because of this, we suggest directly modeling the sequence of random partitions when clustering is of principal interest. To this end, we develop a class of dependent random partition models that explicitly models dependence in a sequence of partitions. We derive conditional and marginal properties of the joint partition model and devise computational strategies when employing the method in Bayesian modeling. In the case of temporal dependence, we demonstrate through simulation how the methodology produces partitions that evolve gently and naturally over time. We further illustrate the utility of the method by applying it to an environmental dataset that exhibits spatio-temporal dependence. Supplemental files for this article are available online.

摘要

我们考虑对随机分区的依赖序列进行建模。众所周知，在贝叶斯非参数中，离散类型的随机测量会导致随机分区上的分布。因此，社区假设获得随机分区的相关序列的最佳方法是通过对相关随机度量进行建模。我们认为这种方法是有问题的，并表明由相关贝叶斯非参数先验诱导的随机分区模型表现出分区之间的反直觉依赖性，即使对随机概率测量序列的依赖性是直观的。因此，我们建议在主要关注聚类时直接对随机分区序列进行建模。为此，我们开发了一类依赖随机分区模型，它显式地对分区序列中的依赖关系进行建模。我们推导出联合分区模型的条件和边际属性，并在贝叶斯建模中采用该方法时设计计算策略。在时间依赖性的情况下，我们通过模拟演示该方法如何产生随着时间缓慢而自然地演变的分区。我们通过将其应用于表现出时空依赖性的环境数据集来进一步说明该方法的实用性。本文的补充文件可在线获取。我们通过模拟展示了该方法如何产生随时间缓慢而自然地演变的分区。我们通过将其应用于表现出时空依赖性的环境数据集来进一步说明该方法的实用性。本文的补充文件可在线获取。我们通过模拟展示了该方法如何产生随时间缓慢而自然地演变的分区。我们通过将其应用于表现出时空依赖性的环境数据集来进一步说明该方法的实用性。本文的补充文件可在线获取。