Surrogate models such as Gaussian processes (GP) have been proposed to accelerate approximate Bayesian computation (ABC) when the statistical model of interest is expensive-to-simulate. In one such promising framework the discrepancy between simulated and observed data is modelled with a GP. 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. Current surrogate-based ABC methods also produce only a point estimate of the ABC posterior while there can be substantial additional uncertainty due to the limited budget of simulations. We also address the problem of quantifying the uncertainty of ABC posterior and discuss the connections between our resulting framework called Bayesian ABC, Bayesian quadrature (BQ) and Bayesian optimisation (BO). Experiments with several toy and real-world simulation models demonstrate advantages of the proposed techniques.

本文提出了一种基于高斯过程的代理模型改进的近似贝叶斯计算方法，同时结合批次-序列贝叶斯试验设计策略实现模型并行化，并通过一种数值方法完整量化不确定性，该方法被称为贝叶斯ABC，并讨论了它与贝叶斯积分和贝叶斯优化之间的联系。

高斯过程代理近似贝叶斯计算中的批量模拟和不确定性量化