Dependent Modeling of Temporal Sequences of Random Partitions
本文指出通过依赖随机测度建模时间序列划分存在反直觉问题，直接提出一类依赖随机划分模型，能自然演化并适用于时空数据聚类。
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.