Approximation of improper prior by vague priors

Christele Bioche (1) , Pierre Druilhet (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We propose a convergence mode for prior distributions which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to a non-informative prior. We consider some cases where vague priors have necessarily large variances and other cases where they have not. We give some constructions of vague priors that approximate the Haar measures or the Jeffreys priors. Then, we study the consequences of the convergence of prior distributions on the posterior analysis. We also revisit the Jeffreys-Lindley paradox.

Mots clés: approximation of improper priors; conjugate priors; convergence of prior; Jeffreys-Lindley paradox; Jeffreys prior; noninformative priors; vague priors.; vague priors

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christele Bioche, Pierre Druilhet. Approximation of improper prior by vague priors. 2013. ⟨hal-00880194⟩