Open Access
September 2021 Sequential Bayesian Experimental Design for Implicit Models via Mutual Information
Steven Kleinegesse, Christopher Drovandi, Michael U. Gutmann
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Bayesian Anal. 16(3): 773-802 (September 2021). DOI: 10.1214/20-BA1225


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. A class of models 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. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.


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Steven Kleinegesse. Christopher Drovandi. Michael U. Gutmann. "Sequential Bayesian Experimental Design for Implicit Models via Mutual Information." Bayesian Anal. 16 (3) 773 - 802, September 2021.


Published: September 2021
First available in Project Euclid: 31 July 2020

MathSciNet: MR4303868
Digital Object Identifier: 10.1214/20-BA1225

Primary: 62K05
Secondary: 62L05

Keywords: Approximate Bayesian Computation , Bayesian experimental design , implicit models , likelihood-free inference , mutual information

Vol.16 • No. 3 • September 2021
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