How many data clusters are in the Galaxy data set? Bayesian cluster analysis in action

TL;DR

This paper investigates how different prior assumptions in Bayesian mixture models influence the estimated number of clusters in the Galaxy data set, providing guidance for more effective and transparent Bayesian clustering.

Contribution

It performs a comprehensive sensitivity analysis of prior specifications in Bayesian mixture models, clarifying their impact on clustering results and offering practical recommendations.

Findings

Prior choices significantly affect the estimated number of clusters.

Certain prior specifications lead to sparser, more interpretable clustering solutions.

Simulation results support recommended prior settings for Bayesian clustering.

Abstract

In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (2001) compares maximum likelihood and Bayesian analyses of the Galaxy data set and expresses reservations about the Bayesian approach due to the fact that the prior assumptions imposed remain rather obscure while playing a major role in the results obtained and conclusions drawn. The aim of the paper is to address Aitkin's concerns about the Bayesian approach by shedding light on how the specified priors influence the number of estimated clusters. We perform a sensitivity analysis of different prior specifications for the mixtures of finite mixture model, i.e., the mixture model where a prior on the number of components is included. We use an extensive set of different prior specifications in a full factorial design and assess their impact on the estimated number of clusters for the Galaxy data set. Results highlight the interaction effects of the prior specifications and provide insights into which prior specifications are recommended to obtain a sparse clustering solution. A simulation study with artificial data provides further empirical evidence to support the recommendations. A clear understanding of the impact of the prior specifications removes restraints preventing the use of Bayesian methods due to the complexity of selecting suitable priors. Also, the regularizing properties of the priors may be intentionally exploited to obtain a suitable clustering solution meeting prior expectations and needs of the application.