Parameter estimation in the context of hierarchical Bayesian models

Abstract:  The Bayesian statistical framework provides a rich and versatile environment to treat ill-posed problems by augmenting the original problem with additional information in the form of priors. Gaussian prior models are often used because they lead to quadratic penalty functions that are easy to handle, but they are proved to be not well suited to provide sparsity favoring penalties. In this talk, natural extensions of Gaussian priors models, conditionally Gaussian prior models, are discussed. The flexibility and usefulness as well as numerical efficiency of this extension is illustrated with an application to magnetoencephalography (MEG).