Informed Bayesian Finite Mixture Models via Asymmetric Dirichlet Priors

TL;DR

This paper introduces a novel Bayesian finite mixture model that allows direct prior elicitation on the number of clusters using an asymmetric Dirichlet prior, improving interpretability and flexibility in clustering applications.

Contribution

It develops a new finite mixture modeling approach with priors on the number of clusters, employing asymmetric Dirichlet distributions and a penalized complexity prior for enhanced prior elicitation.

Findings

The proposed method allows intuitive prior specification on the number of clusters.

Numerical experiments demonstrate the flexibility and effectiveness of the approach.

Real data applications show practical utility in clustering tasks.

Abstract

Finite mixture models are flexible methods that are commonly used for model-based clustering. A recent focus in the model-based clustering literature is to highlight the difference between the number of components in a mixture model and the number of clusters. The number of clusters is more relevant from a practical stand point, but to date, the focus of prior distribution formulation has been on the number of components. In light of this, we develop a finite mixture methodology that permits eliciting prior information directly on the number of clusters in an intuitive way. This is done by employing an asymmetric Dirichlet distribution as a prior on the weights of a finite mixture. Further, a penalized complexity motivated prior is employed for the Dirichlet shape parameter. We illustrate the ease to which prior information can be elicited via our construction and the flexibility of the resulting induced prior on the number of clusters. We also demonstrate the utility of our approach using numerical experiments and two real world data sets.