**Thursday November 5, 2015, room C47**

**14h – 15h** :** Jean-Bernard Salomond** (CEREMADE, Univ. Dauphine)

**Titre** : Sharp conditions for posterior contraction in the Sparse normal means problem **Abstract:** The first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage priors has been proposed. Many of these shrinkage priors can be written as a scale mixture of normals, which makes them particularly easy to implement. We propose sharp general conditions on the prior on the local variance in scale mixtures of normals, such that posterior contraction at the minimax rate is assured. The conditions require tails at least as heavy as Laplace, but not too heavy, and a large amount of mass around zero relative to the tails, more so as the sparsity increases. These conditions give some general guidelines for choosing a shrinkage prior for estimation under a nearly black sparsity assumption. We verify these conditions for Horseshoe type class of priors which includes the horseshoe and the normal-exponential gamma priors, and for the horseshoe+, the inverse-Gaussian prior, the normal-gamma prior, and the spike-and-slab Lasso, and thus extend the number of shrinkage priors which are known to lead to posterior contraction at the minimax estimation rate. (Joint work with Stéphanie van der Pas and Johannes Schmidt-Heiber)

**15h -15h30** : **Moussab Djerrab** (LTCI, Telecom ParisTech)

**Titre** : Structured prediction with operator-valued kernels **Abstract:** Operator valued Kernel are gaining momentum in the scientific community. We propose to use this framework to solve prediction problems for structured data. We are currently working on a chain of work for modelling the data and predicting it. In this talk, I will present my exploratory work on theses topics with a focus on the future developments.