Maximum cross-entropy and prior distributions.

Han-Ping Li (1)

1 IRMA - Institut de Recherche Mathématique Avancée

A maximum cross-entropy method for determining the reference prior distribution, which represents partial information or complete ignorance, is proposed and studied in this paper, several properties and interpretations are given. Some sufficient conditions for a prior to be the reference distribution or $epsilon-!$ reference distribution are given, these sufficient conditions turn out to be also necessary within some convex class of prior distributions. Besides some theoretical results, attention is also paid to the applications to Bernoulli model, Binomial model, Poisson process, Translation-scale model and Elliptic model. In the case of group models, we find left Haar measure as the reference prior distribution.

Mots clés: Ignorance prior; Reference prior; Jeffreys prior; Left Haar measure"; Maximum cross-entropy; Left Haar measure; "Maximum cross-entropy

Domaines: Statistiques [math.ST]

Han-Ping Li. Maximum cross-entropy and prior distributions.. 1997. ⟨hal-00129565⟩