Jeffreys priors for mixture estimation: properties and alternatives

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. The implementation and the properties of Jeffreys priors in several mixture settings are studied. It is shown that the associated posterior distributions most often are improper. Nevertheless, the Jeffreys prior for the mixture weights conditionally on the parameters of the mixture components will be shown to have the property of conservativeness with respect to the number of components, in case of overfitted mixture and it can be therefore used as a default priors in this context.