B1375
Title: Dependent modeling of temporal sequences of random partitions
Authors: David Dahl - Brigham Young University (United States) [presenting]
Richard Warr - Brigham Young University (United States)
Thomas Jensen - Brigham Young University (United States)
Abstract: Modelling a dependent sequence of random partitions is considered. 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 modelling dependent random measures. It is argued that this approach is problematic and is shown 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, directly modelling the sequence of random partitions is suggested when clustering is of principal interest. To this end, a class of dependent random partition models is developed that explicitly model dependence in a sequence of partitions. Conditional and marginal properties of the joint partition model and computational strategies are derived when employing the method in Bayesian modelling. In the case of temporal dependence, through simulation, it is demonstrated how the methodology produces partitions that evolve gently and naturally over time. The utility of the method is further illustrated by applying it to an environmental dataset that exhibits spatiotemporal dependence.
