There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations in terms of Exchangeable Partition Probability Functions (EPPF). Gibbs-type priors encompass a broad class of such cases, including Dirichlet and Pitman-Yor processes. Even though there have been some proposals to relax the exchangeability assumption, allowing covariate-dependence and partial exchangeability, limited consideration has been given on how to include concrete prior knowledge on the partition. For example, we are motivated by an epidemiological application, in which we wish to cluster birth defects into groups and we have prior knowledge of an initial clustering provided by experts. As a general approach for including such prior knowledge, we propose a Centered Partition (CP) process that modifies the EPPF to favor partitions close to an initial one. Some properties of the CP prior are described, a general algorithm for posterior computation is developed, and we illustrate the methodology through simulation examples and an application to the motivating epidemiology study of birth defects.
This work was supported through cooperative agreements under R01ES027498, PA 96043, PA 02081 and FOA DD09-001 from the Centers for Disease Control and Prevention (CDC) to the North Carolina Center for Birth Defects Research and Prevention at the University of North Carolina at Chapel Hill, and to other Centers for Birth Defects Research and Prevention participating in the National Birth Defects Prevention Study and/or the Birth Defects Study to Evaluate Pregnancy Exposures.
"Centered Partition Processes: Informative Priors for Clustering (with Discussion)." Bayesian Anal. 16 (1) 301 - 370, March 2021. https://doi.org/10.1214/20-BA1197