We present a framework for approximate Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex models. We model the log-likelihood function using a Gaussian process (GP) and the main methodological innovation is to apply this model to emulate the progression that an exact Metropolis-Hastings (MH) sampler would take if it was applicable. Informative log-likelihood evaluation locations are selected using a sequential experimental design strategy until the MH accept/reject decision is done accurately enough according to the GP model. The resulting approximate sampler is conceptually simple and sample-efficient. It is also more robust to violations of GP modelling assumptions compared with earlier, related "Bayesian optimisation-like" methods tailored for Bayesian inference. We discuss some theoretical aspects and various interpretations of the resulting approximate MH sampler, and demonstrate its benefits in the context of Bayesian and generalised Bayesian likelihood-free inference for simulator-based statistical models.

翻译：我们提出了一种在计算约束下仅能获得有限数量含噪对数似然评估时的近似贝叶斯推断框架，这一情形在复杂模型应用中日益普遍。我们采用高斯过程对对数似然函数进行建模，核心方法创新在于运用该模型模拟精确Metropolis-Hastings (MH)采样器在适用情况下本应遵循的演进过程。通过序贯实验设计策略选择具有信息量的对数似然评估位置，直至MH接受/拒绝判定在GP模型下达到足够精确。该近似采样器概念简洁且样本高效，相较于早期针对贝叶斯推断的“贝叶斯优化类”方法，其对GP建模假设的违反更具鲁棒性。我们讨论了由此产生的近似MH采样器的若干理论层面与多种解释，并在基于模拟器统计模型的贝叶斯及广义贝叶斯无似然推断背景下展示了其优势。