B1321
Title: Dependent random partitions by shrinking towards an anchor
Authors: Richard Warr - Brigham Young University (United States) [presenting]
Abstract: Random partition models are flexible Bayesian prior distributions which accommodate heterogeneity and the borrowing of strength by postulating that data are generated from latent clusters. The Chinese restaurant process and other stick-breaking priors are popular exchangeable random partition models used in Bayesian nonparametric. The exchangeability assumption is not appropriate when one has a notation of which items are likely to be clustered together. It is called the best guess partition, the anchor partition. It defines the shrinkage partition (SP) distribution that takes any random partition distribution and pulls its probability mass towards the anchor partition. Since prior knowledge about item clustering may differ across the items, the formulation allows for differential shrinkage towards the anchor. The distribution has a tractable normalizing constant and easily fits into standard Markov chain Monte Carlo sampling algorithms for model fitting. The properties of the SP distribution are explored and compared to related random partition distributions. It shows how the SP distribution provides a general framework to build dependent random partition models and demonstrates the method in the application of hierarchically-dependent and time-dependent random partitions.
