On a Loss-based prior for the number of components in mixture models

TL;DR

This paper introduces a loss-based prior for the number of components in finite mixture models, offering a flexible, easy-to-implement approach that incorporates prior knowledge and improves model selection.

Contribution

It presents a novel loss-based prior for mixture components, enhancing prior specification flexibility and demonstrating competitive performance against existing methods.

Findings

The proposed prior performs well on real and simulated data.

It effectively incorporates prior information into model selection.

The method is computationally straightforward and adaptable.

Abstract

We propose a prior distribution for the number of components of a finite mixture model. The novelty is that the prior distribution is obtained by considering the loss one would incur if the true value representing the number of components were not considered. The prior has an elegant and easy to implement structure, which allows to naturally include any prior information one may have as well as to opt for a default solution in cases where this information is not available. The performance of the prior, and comparison with existing alternatives, is studied through the analysis of both real and simulated data.