Bayesian cluster analysis: Point estimation and credible balls

TL;DR

This paper develops methods for summarizing Bayesian clustering posteriors using point estimates and credible sets, addressing visualization and uncertainty quantification challenges.

Contribution

It introduces decision and information theoretic techniques to create meaningful summaries of Bayesian clustering posteriors, including credible balls.

Findings

Proposes new point estimation methods for Bayesian clustering.

Develops credible sets to quantify uncertainty in clustering.

Enhances visualization of posterior distributions in clustering analysis.

Abstract

Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over the entire space of partitions, allowing one to assess statistical properties, such as uncertainty on the number of clusters. However, an important problem is how to summarize the posterior; the huge dimension of partition space and difficulties in visualizing it add to this problem. In a Bayesian analysis, the posterior of a real-valued parameter of interest is often summarized by reporting a point estimate such as the posterior mean along with 95% credible intervals to characterize uncertainty. In this paper, we extend these ideas to develop appropriate point estimates and credible sets to summarize the posterior of clustering structure based on decision and information theoretic techniques.