# Centered Partition Process: Informative Priors for Clustering

## TL;DR

This paper introduces a Centered Partition process that incorporates prior expert knowledge into Bayesian clustering, allowing for more informed and flexible partitioning, demonstrated through simulations and an epidemiological case study.

## Contribution

It proposes a novel Centered Partition prior that modifies EPPF to include prior knowledge, enhancing Bayesian clustering methods.

## Key findings

- The CP prior effectively incorporates prior knowledge into clustering.
- The methodology performs well in simulations and real epidemiological data.
- The approach offers a flexible way to include expert input in Bayesian models.

## 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.