We propose a posterior for Bayesian Likelihood-Free Inference (LFI) based on generalized Bayesian inference. To define the posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. In LFI, we can sample from the model but not evaluate the likelihood; hence, we employ SRs which admit unbiased empirical estimates. We use the Energy and Kernel SRs, for which our posterior enjoys consistency in a well-specified setting and outlier robustness. We perform inference with pseudo-marginal (PM) Markov Chain Monte Carlo (MCMC) or stochastic-gradient (SG) MCMC. While PM-MCMC works satisfactorily for simple setups, it mixes poorly for concentrated targets. Conversely, SG-MCMC requires differentiating the simulator model but improves performance over PM-MCMC when both work and scales to higher-dimensional setups as it is rejection-free. Although both techniques target the SR posterior approximately, the error diminishes as the number of model simulations at each MCMC step increases. In our simulations, we employ automatic differentiation to effortlessly differentiate the simulator model. We compare our posterior with related approaches on standard benchmarks and a chaotic dynamical system from meteorology, for which SG-MCMC allows inferring the parameters of a neural network used to parametrize a part of the update equations of the dynamical system.

翻译：基于广义贝叶斯推断，我们提出了一种适用于贝叶斯无似然推断（LFI）的后验分布。为定义该后验，我们采用评分规则（SRs），其通过给定观测值对概率模型进行评估。在LFI中，我们可从模型中进行采样但无法计算似然函数；因此，我们采用能够获得无偏经验估计的评分规则。我们使用能量评分规则和核评分规则，在这些规则下，我们的后验分布兼具良好设定情形下的相合性与异常值鲁棒性。我们通过伪边际（PM）马尔可夫链蒙特卡洛（MCMC）或随机梯度（SG）MCMC进行推断。PM-MCMC在简单设置下表现良好，但对于集中目标分布混合效果较差。相比之下，SG-MCMC需要对仿真模型进行微分，但在两者均适用时性能优于PM-MCMC，且因无拒绝抽样机制可扩展至更高维设置。尽管两种方法均近似逼近评分规则后验，但误差会随着每个MCMC步中模型模拟次数的增加而减小。在仿真中，我们利用自动微分轻松对仿真模型进行求导。我们将提出的后验与相关方法在标准基准测试及一个气象学混沌动力系统上进行比较，其中SG-MCMC可用于推断用于参数化动力系统更新方程部分的神经网络参数。