Shrinking a partition distribution towards a baseline partition, with applications to dependent partitions
Random partition models are closely related to Bayesian nonparametric models and provide flexible means to borrow strength in Bayesian data analysis. Parsimony is obtained by postulating that observations share model parameters with other observations belonging to the same cluster in a latent partition. In many contexts, prior knowledge regarding the partitioning of observations may be available and we may desire to use this baseline partition information to influence the prior partition distribution. To this end, we propose the shrinkage partition distribution (SPD) which shrinks any baseline partition distribution towards a baseline partition. Recognizing that prior knowledge may be stronger for some items than others, our formulation allows for item-specific shrinkage towards the baseline partition. Further, our approach has a tractable normalizing constant, permitting posterior inference on the shrinkage and parameters associated with the baseline distribution. We explore the properties of our proposed distribution and other comparable distributions. We also show how the SPD can hierarchically model a collection of random partition distributions and can also model time-dependent random partitions. This is joint work with Richard L. Warr and Thomas P. Jensen.