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

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Paganin, S; Herring, AH; Olshan, AF; Dunson, DB; National Birth Defects Prevention Study,

Published Date

  • March 2021

Published In

Volume / Issue

  • 16 / 1

Start / End Page

  • 301 - 370

PubMed ID

  • 35958029

Pubmed Central ID

  • PMC9364237

Electronic International Standard Serial Number (EISSN)

  • 1931-6690

International Standard Serial Number (ISSN)

  • 1936-0975

Digital Object Identifier (DOI)

  • 10.1214/20-ba1197

Language

  • eng