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Title: Uncertainty quantification and computational methods for the spike and slab prior Authors:  Botond Szabo - Leiden University (Netherlands) [presenting]
Ismael Castillo - Sorbonne Universite (France)
Tim van Erven - University Paris-Sud and INRIA (France)
Abstract: Spike and slab priors are frequently used in various fields of applications to induce sparsity in high-dimensional models. It is well known that sampling from the corresponding posterior distribution is computationally very demanding and accurate methods with theoretical guarantees break down on small sample and feature sizes. In practice therefore approximation algorithms were suggested based on optimisation methods. These methods have, however, only limited theoretical underpinning. Firstly, we introduce accurate (analytic) computational methods in the context of the Gaussian sequence model, which can handle moderately large dimensional parameters. Secondly, we will investigate how reliable are the Bayesian uncertainty statements using spike-and-slab priors from a frequentist perspective, again in the context of the Gaussian sequence model. We will derive sufficient and (in some sense) necessary condition under which Bayesian credible sets provide reliable confidence statements.