We present an efficient approach for doing approximate Bayesian inference when only a limited number of noisy likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex models. Our main methodological innovation is to model the log-likelihood function using a Gaussian process (GP) in a local fashion and apply this model to emulate the progression that an exact Metropolis-Hastings (MH) algorithm would take if it was applicable. New log-likelihood evaluation locations are selected using sequential experimental design strategies such that each MH accept/reject decision is done within a pre-specified error tolerance. The resulting approach is conceptually simple and sample-efficient as it takes full advantage of the GP model. It is also more robust to violations of GP modelling assumptions and better suited for the typical situation where the posterior is substantially more concentrated than the prior, compared with various existing inference methods based on global GP surrogate modelling. We discuss the probabilistic interpretations and central theoretical aspects of our approach, and we then demonstrate the benefits of the resulting algorithm in the context of likelihood-free inference for simulator-based statistical models.

翻译：我们提出一种有效的方法,在由于计算限制而只能获得有限数量的噪音可能性评估的情况下,进行近似贝雅斯推断,因为计算限制越来越常见,而计算限制越来越常见。我们的主要方法创新是以当地方式模拟使用高斯进程(GP)的日志相似性功能,并应用这一模型来模仿精确的大都会-豪斯(MH)算法(如果适用的话)的演进。新的日志相似性评价地点是使用连续的实验设计战略选择的,例如每个MH接受/拒绝决定都是在预先确定的差错容忍度内作出的。由此产生的方法在概念上是简单而具有样本效率的,因为它充分利用了GP模式的优势。它还更能应对违反GP建模假设的情况,更适合典型的情况,即远地点远地点比以前更加集中,而现有的各种基于全球GPsug模型的推论方法则更为合适。我们讨论了我们方法的概率解释和核心理论方面,然后我们展示在基于可能性的统计模型的模拟范围内产生的算法的好处。