We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics 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 exhibit counter-intuitive dependence among partitions even though the dependence for the sequence of random probability measures is intuitive. Because of this, we advocate instead to model the sequence of random partitions directly 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 data set that exhibits spatio-temporal dependence.
翻译:我们考虑了随机分区依附序列的建模任务。 众所周知, 巴伊西亚非参数的随机测量导致随机分区的分布。 因此, 社区认为, 获得随机分区依附序列的最佳办法是通过依附随机测量进行建模。 我们争辩说, 这种方法存在问题, 并表明, 由贝伊西亚依附性非参数前端引起的随机分区模型在分区间表现出反直觉依赖性, 尽管随机概率测量序列的依附性是直视的。 因此, 我们主张在聚在一起是主要利益时直接模拟随机分区的序列。 为此, 我们开发了一种依附随机分区模型的分类。 我们从联合分区模型中得出有条件和边际特性, 在采用贝伊斯模型方法时设计计算策略。 在时间依赖性方面, 我们通过模拟该方法如何产生随时间而温和自然演变的分区。 我们进一步说明该方法的效用, 将它应用于一个环境数据集中, 以显示空间- 视界系依赖性 。