Sequential Bayesian Experimental Design for Implicit Models via Mutual Information

• Activity Number: 6 - Highlights in 'Bayesian Analysis': Stories to Tell
• Type: Invited
• Date/Time: Sunday, August 8, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Steven Kleinegesse* and Michael Urs Gutmann and Christopher Drovandi
• Companies: The University of Edinburgh, School of Informatics and The University of Edinburgh, School of Informatics and Queensland University of Technology, School of Mathematical Sciences
• Keywords: Bayesian experimental design; likelihood-free inference; mutual information; approximate Bayesian computation; implicit models

Abstract

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. Of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI, optimised via Bayesian Optimisation.