Jeffreys priors for mixture estimation: properties and alternatives

摘要

While Jeffreys priors usually are well-defined for the parameters of mixturesof distributions, they are not available in closed form. Furthermore, theyoften are improper priors. Hence, they have never been used to draw inferenceon the mixture parameters. The implementation and the properties of Jeffreyspriors in several mixture settings are studied. It is shown that the associatedposterior distributions most often are improper. Nevertheless, the Jeffreysprior for the mixture weights conditionally on the parameters of the mixturecomponents will be shown to have the property of conservativeness with respectto the number of components, in case of overfitted mixture and it can betherefore used as a default priors in this context.