Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the Approximate Bayesian Computation (ABC) based inference. To advance the possibilities for performing likelihood-free inference in higher dimensional parameter spaces, we introduce an extension of the popular Bayesian optimisation based approach to approximate discrepancy functions in a probabilistic manner which lends itself to an efficient exploration of the parameter space. Our approach achieves computational scalability for higher dimensional parameter spaces by using separate acquisition functions and discrepancies for each parameter. The efficient additive acquisition structure is combined with exponentiated loss -likelihood to provide a misspecification-robust characterisation of the marginal posterior distribution for all model parameters. The method successfully performs computationally efficient inference in a 100-dimensional space on canonical examples and compares favourably to existing modularised ABC methods. We further illustrate the potential of this approach by fitting a bacterial transmission dynamics model to a real data set, which provides biologically coherent results on strain competition in a 30-dimensional parameter space.

翻译：基于模拟器的统计模型的无似然推断已从初期阶段迅速发展为从业者的实用工具。然而，对于参数数量超过若干个的模型，基于近似贝叶斯计算（ABC）的推断仍普遍面临挑战。为推进高维参数空间中无似然推断的可能性，我们提出了一种基于贝叶斯优化的流行方法的扩展，以概率方式近似差异函数，从而高效探索参数空间。该方法通过为每个参数分别使用采集函数和差异函数，实现了高维参数空间的计算可扩展性。高效的加性采集结构与指数化损失-似然相结合，为所有模型参数的边际后验分布提供了误设定鲁棒的表征。该方法在典型示例的100维空间中成功实现了计算高效的推断，并与现有模块化ABC方法相比表现优异。我们进一步通过将细菌传播动力学模型拟合至真实数据集，展示了该方法的潜力，在30维参数空间中生成了关于菌株竞争的生物学一致结果。