Jeffreys priors for mixture estimation

TL;DR

This paper investigates the use of Jeffreys priors in mixture models, highlighting their limitations and proposing a practical noninformative alternative for inference.

Contribution

It analyzes the properties of Jeffreys priors in mixture estimation and introduces a new noninformative prior to address their shortcomings.

Findings

Jeffreys priors often lead to improper posteriors in mixture models

Explicit forms of Jeffreys priors are generally unavailable

A noninformative alternative improves mixture inference

Abstract

While Jeffreys priors usually are well-defined for the parameters of mixtures of distributions, they are not available in closed form. Furthermore, they often are improper priors. Hence, they have never been used to draw inference on the mixture parameters. We study in this paper the implementation and the properties of Jeffreys priors in several mixture settings, show that the associated posterior distributions most often are improper, and then propose a noninformative alternative for the analysis of mixtures.