Batch simulations and uncertainty quantification in Gaussian process surrogate-based approximate Bayesian computation

Marko Järvenpää, Aki Vehtari, Pekka Marttinen

Keywords: approximate Bayesian computation, Gaussian processes, surrogate models, experimental design, uncertainty quantification

TL;DR: We propose principled batch Bayesian experimental design strategies and a method for uncertainty quantification of the posterior summaries in a Gaussian process surrogate-based approximate Bayesian computation framework.

Abstract: Surrogate models can be used to accelerate approximate Bayesian computation (ABC). In one such framework the discrepancy between simulated and observed data is modelled with a Gaussian process. So far principled strategies have been proposed only for sequential selection of the simulation locations. To address this limitation, we develop Bayesian optimal design strategies to parallellise the expensive simulations. We also touch the problem of quantifying the uncertainty of the ABC posterior due to the limited budget of simulations.