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：基于模拟器统计模型的无似然推断已从初期迅速发展到成为实践者的有用工具。然而，涉及多个参数的模型通常仍是近似贝叶斯计算（ABC）推断的挑战。为了推动在高维参数空间中进行无似然推断的可能性，我们引入了一种流行的基于贝叶斯优化的方法的扩展，以概率方式逼近差异函数，从而实现对参数空间的高效探索。我们的方法通过为每个参数使用独立的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。高效的加法采集结构与指数化损失似然相结合，为所有模型参数的边缘后验分布提供了鲁棒性误设的特征。该方法在典型示例中成功地在100维空间中进行计算高效的推断，且优于现有的模块化ABC方法。我们进一步通过将细菌传播动力学模型拟合到真实数据集来说明该方法的潜力，在30维参数空间中生成了关于菌株竞争的生物一致性结果。