  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.
