In this work we will present a general Theorem to obtain a Bernstein - von Mises property for the posterior distribution in infinite dimensional models, when the parameter of interest is a finite dimensional functional of the parameter of interest. The aim of this work is to study functionals which are not necessarily linear. The special case of the functional equal to the L2 norm of the regression function in a regression model will be considered. Various families of nonparametris priors will also be studied. The Bernstein von Mises property means that the posterior distribution behaves asymptotically like a Gaussian distribution and has interesting implications.
Keywords: Bayesian nonparametric; Bernstein von Mises; Non linear functionals; Asymptotic
Biography: Judith Rousseau is professor at University Paris Dauphine and at ENSAE. She works on Bayesian statistics and a major part of her work is on the frequentist properties of Bayesian nonparametrics methods.