Proximity penalty priors for Bayesian mixture models

TL;DR

This paper introduces proximity penalty priors (PPPs), a flexible Bayesian framework that encodes prior beliefs about component relationships in mixture models without arbitrary thresholds, influencing posterior inference.

Contribution

The paper proposes a novel, scale-free prior framework called PPPs that explicitly incorporates component proximity preferences in Bayesian mixture models.

Findings

PPPs effectively encode prior beliefs about component relationships.

PPPs influence posterior distributions in simulated and real data.

The approach is theoretically valid and minimally restrictive.

Abstract

When using mixture models it may be the case that the modeller has a-priori beliefs or desires about what the components of the mixture should represent. For example, if a mixture of normal densities is to be fitted to some data, it may be desirable for components to focus on capturing differences in location rather than scale. We introduce a framework called proximity penalty priors (PPPs) that allows this preference to be made explicit in the prior information. The approach is scale-free and imposes minimal restrictions on the posterior; in particular no arbitrary thresholds need to be set. We show the theoretical validity of the approach, and demonstrate the effects of using PPPs on posterior distributions with simulated and real data.