Lieu : IHP, Amphithéâtre Hermite.
14h00: Jean-Bernard Salomond (CWI, Amsterdam)
Titre : General approach to posterior contraction in nonparametric inverse problems
Résumé : When considering non-parametric problems from a Bayesian point of view, it is crucial to understand the behaviour of the posterior distribution since the prior is not always swamped by the data in these models. A way to insure that inference based on the posterior distribution is not dramatically wrong is to verify that the posterior has good asymptotic properties, such as consistency. The study of the rate at which the posterior contract around the true distribution gives a better understanding of the impact of the prior on the posterior distribution.
There is a wide literature on posterior contraction for non-parametric problems. In particular, general conditions on the prior such that the posterior contracts at a given rate have been proposed for many types of models. However, only few results are known for ill-posed inverse problems. In this work, we propose general conditions on the prior to derive posterior contraction rate in this case. Our approach not only generalises the results obtained in the Bayesian literature, but also allows us to consider models that were not covered by the existing theory.
15h00: Nathalie Villa-Vialaneix (INRA de Toulouse)
Titre : Inferring networks from multiple samples with consensus LASSO
Résumé : Networks are very useful tools to decipher complex regulatory relationships between genes in an organism. Most work address this issue
in the context of i.i.d., treated vs. control or time-series samples. However, many data sets include expression obtained for the same cell type of an organism, but in several conditions. We introduce a novel method for inferring networks from samples obtained in various but related experimental conditions. This approach is based on a double penalization: a first penalty aims at controlling the global sparsity of the solution whilst a second penalty is used to make condition-specific networks consistent with a consensual network. This “consensual network” is introduced to represent the dependency structure between genes, which is shared by all conditions. We show that different “consensus” penalties can be used, some integrating prior (e.g., bibliographic) knowledge and others that are adapted along the optimization scheme. In all situations, the proposed double penalty can be expressed in terms of a LASSO problem and hence, solved using standard approaches which address quadratic problems with L 1
-regularization. This approach is combined with a bootstrap approach and is made available in the R package therese. Our proposal is illustrated
on simulated datasets and compared with independent estimations and alternative methods. It is also applied to a real dataset to emphasize
the differences in regulatory networks before and after a low-calorie diet.
16h00: Marco Oesting (AgroParisTech)
Titre : Statistical Post-Processing of Forecasts for Extreme Wind Gusts
Résumé : Extreme value theory aims at the prediction of rare events. In the context of weather forecasting, focusing on extremes is the prediction of events that are rare under given or predicted weather conditions. We present a model that allows to post-process the numerical forecast for extreme wind gusts by simulating wind gusts conditional on the forecast. Here, the marginal distributions and dependence structure are modeled separately. In order to incorporate the dependence between the spatial random fields of observed and forecasted maximal wind gusts, we propose to model them jointly by a bivariate Brown-Resnick process which is characterized by the underlying pseudo cross-variogram. The model is applied to real observation and forecast data for stations in Northern Germany. The resulting post-processed forecasts are verified.
This is joint work with Martin Schlather (University of Mannheim) and Petra Friederichs (University of Bonn).