Parallel Gaussian Process Surrogate Bayesian Inference with Noisy Likelihood Evaluations

We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method is used form the estimates using computationally costly forward simulations. frame task as sequential experimental design problem, where function modelled with hierarchical Gaussian process (GP) surrogate model, which efficiently select additional evaluation locations. Motivated by recent progress in related problem batch optimisation, we develop various batch-sequential strategies allow run some potentially simulations parallel. analyse properties resulting theoretically empirically. Experiments several toy problems simulation suggest that our robust, highly parallelisable, sample-efficient.