We propose a framework for Bayesian Likelihood-Free Inference (LFI) based on Generalized Bayesian Inference using scoring rules (SRs). SRs are used to evaluate probabilistic models given an observation; a proper SR is minimised in expectation when the model corresponds to the data generating process for the observations. Using a strictly proper SR, for which the above minimum is unique, ensures posterior consistency of our method. Further, we prove finite sample posterior consistency and outlier robustness of our posterior for the Kernel and Energy Scores. As the likelihood function is intractable for LFI, we employ consistent estimators of SRs using model simulations in a pseudo-marginal MCMC; we show the target of such chain converges to the exact SR posterior by increasing the number of simulations. Furthermore, we note popular LFI techniques such as Bayesian Synthetic Likelihood (BSL) can be seen as special cases of our framework using only proper (but not strictly so) SR. We empirically validate our consistency and outlier robustness results and show how related approaches do not enjoy these properties. Practically, we use the Energy and Kernel Scores, but our general framework sets the stage for extensions with other scoring rules.

翻译：我们建议采用评分规则(SRs),根据通用贝耶斯推理法,为贝耶斯河沿岸无隐性推断(LFI)提供一个框架。 使用员工代表法来评估观察到的概率模型; 当模型与观测数据生成过程相匹配时,适当的员工代表法在期望值中被最小化。 使用严格的适当的员工代表法(上述最低数值是独一无二的),确保了我们方法的后继一致性。 此外,我们证明我们框架的后继性(后继性)一致性和超强性(LFI)是有限的样本。 由于可能性功能对员工代表法是难以确定的,我们使用模拟模型模拟的模拟模型来评估员工代表法;我们通过增加模拟次数来显示这种链的目标与准确的员工代表法相趋同。 此外,我们注意到广受欢迎的LFI技术,如Bayesian Syntheticalligood(BSL),可以被视为我们框架的特殊案例,只有适当(但并非严格如此)SR。 我们从实证上验证我们的一致性和超值标准框架,我们如何享受其他的能源标准。