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Centered Partition Processes: Informative Priors for Clustering (with Discussion)

Citation

Paganin, Sally; Herring, Amy H.; Olshan, Andrew F.; & Dunson, David B. (2021). Centered Partition Processes: Informative Priors for Clustering (with Discussion). Bayesian Analysis, 16(1), 301-370.

Abstract

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.

URL

https://doi.org/10.1214/20-BA1197

Reference Type

Journal Article

Article Type

Regular

Year Published

2021

Journal Title

Bayesian Analysis

Author(s)

Paganin, Sally
Herring, Amy H.
Olshan, Andrew F.
Dunson, David B.