Frequentist Analysis of the Posterior for High-Dimensional Models
主 题: Frequentist Analysis of the Posterior for High-Dimensional Models
报告人: Johannes Schmidt-Hieber (Leiden University)
时 间: 2016-12-29 14:00 - 15:00
地 点: 理科一号楼1303
Recently, various methods have been proposed for estimation and model selection in high-dimensional statistical settings. The most widely known procedure is the LASSO which can be interpreted as a maximum a posteriori probability estimate. Generalizing this, it seems natural to study high-dimensional statistics using the Bayesian method. In the first part of the talk, we summarise recent results concerning posterior shrinkage and model selection for spike-and-slab type priors. These methods are known to perform well theoretically but are hard to compute. The second part of the talk is devoted to priors which can be represented as scale mixtures of normals. The well-known horseshoe prior is for instance of this form. We derive sharp conditions under which such priors are sparsity inducing and show some simulations. This is joint work with Stéphanie van der Pas (Leiden), JB Salomond (Paris), Aad van der Vaart (Leiden) and Ismael Castillo (Paris VI). About the speaker: Dr. Johannes Schmidt-Hieber is Assistant Professor at the Mathematical Institute of Leiden University. He received his Ph.D. from the University of G?ttingen and the University of Bern in 2010. His main research interests are nonparametric statistics and Bayesian nonparametrics. He has published more than 10 papers on prestigious journals such as the Annals of Statistics, Electronic Journal of Statistics, and Bernoulli.