Title: The role of sparsity and misspecification in Bayesian model selection
Authors: David Rossell - Universitat Pompeu Fabra (Spain) [presenting]
Francisco Javier Rubio - King's College London (United Kingdom)
Abstract: The state-of-the-art in Bayesian model selection is to induce sparsity to ensure that, asymptotically, one is able to select the optimal model with probability one. Sparsity can be induced either via placing high prior probabilities on small models, setting large prior dispersion (diffuse priors) or using non-local priors. We present recent theoretical and empirical results showing potential adverse effects of using overly sparse priors. We also discuss how these issues are compounded with model misspecification, which we illustrate typically results in a loss of power to detect truly relevant signals. As part of our theoretical results we provide simple rates to help understand how fast one can recover the desired model. We also show a form of asymptotically valid uncertainty quantification for the selected model that is also valuable for L0-penalized regression, the effects of failing to record relevant variables and potential issues with censored data in survival frameworks. We illustrate the practical relevance of these results via empirical studies.