Likelihood-Free Extensions for Bayesian Sequentially Designed Experiments
When considering a Bayesian sequential design framework, sequential Monte Carlo (SMC) algorithms are a natural approach. However, these algorithms require the likelihood function to be evaluated. Therefore, they cannot be applied in cases where the likelihood is not available or is intractable. To overcome this limitation, we propose likelihood-free extensions of the standard SMC algorithm. We also investigate a specific simulation-based approximation of the likelihood known as the synthetic likelihood. The algorithms are applied and tested on a well-studied sequential design problem for estimating a non-linear function of linear regression parameters.
We thank Werner G. Müller for suggesting the illustrative example and three anonymous reviewers for their helpful comments. Markus Hainy has been supported by the French Science Fund (ANR) and Austrian Science Fund (FWF) bilateral grant I-833-N18. Christopher Drovandi was supported by an Australian Research Council’s Discovery Early Career Researcher Award funding scheme (DE160100741).
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