A new criterion for prior probabilities

Cristofaro Rodolfo De (1) , Bruno Lecoutre (2)

1 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

Howson and Urbach (1996) wrote a carefully structured book supporting the Bayesian view of scienti c reasoning, which includes an unfavorable judgment about the so-called objective Bayesian inference. In this paper, the theses of the book are investigated from Carnap's analytical viewpoint in the light of a new formulation of the Principle of Indi fference. In particular, the paper contests the thesis according to which no theory can adequately represent 'ignorance' between alternatives. Beginning from the new formulation of the principle, a criterion for the choice of an objective prior is suggested in the paper together with an illustration for the case of Binomial sampling. In particular, it will be shown that the new prior provides better frequentist properties than the Je ffreys interval.

Mots clés: Data translated likelihood; Frequentist properties; Inductive logic; Jeff reys-rule; Likelihood principle; Objective Bayesian analysis; Principle of indiff erence; Stopping rule

Domaines: Méthodologie [stat.ME]

Cristofaro Rodolfo De, Bruno Lecoutre. A new criterion for prior probabilities. 2010. ⟨hal-00911175⟩