We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method is used to form the noisy log-likelihood estimates using computationally costly forward simulations. We frame the inference task as a sequential Bayesian experimental design problem, where the log-likelihood function is modelled with a hierarchical Gaussian process (GP) surrogate model, which is used to efficiently select additional log-likelihood evaluation locations. Motivated by recent progress in the related problem of batch Bayesian optimisation, we develop various batch-sequential design strategies which allow to run some of the potentially costly simulations in parallel. We analyse the properties of the resulting method theoretically and empirically. Experiments with several toy problems and simulation models suggest that our method is robust, highly parallelisable, and sample-efficient.
The authors are grateful to an associate editor and two anonymous reviewers for their constructive feedback that helped to significantly improve this article. This work was funded by the Academy of Finland (grants no. 286607 and 294015 to PM). We acknowledge the computational resources provided by Aalto Science-IT project.
"Parallel Gaussian Process Surrogate Bayesian Inference with Noisy Likelihood Evaluations." Bayesian Anal. 16 (1) 147 - 178, March 2021. https://doi.org/10.1214/20-BA1200