Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI). However, the existing algorithms can yield overconfident posteriors (Hermans *et al.*, 2022) defeating the whole purpose of credibility if the uncertainty quantification is inaccurate. We propose to include a calibration term directly into the training objective of the neural model in selected amortized SBI techniques. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. The proposed method is not tied to any particular neural model and brings moderate computational overhead compared to the profits it introduces. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference. We empirically show on six benchmark problems that the proposed method achieves competitive or better results in terms of coverage and expected posterior density than the previously existing approaches.

翻译：贝叶斯推理允许在给定先验信息和证据似然的情况下，表达概率模型下后验信念的不确定性。通常情况下，似然函数仅由模拟器隐式定义，因此需要基于模拟的推理（SBI）。然而，现有算法可能产生过度自信的后验分布（Hermans 等，2022），若不确定性量化不准确，则会使可信度的根本目的失效。我们提出将校准项直接纳入选定摊销式SBI技术的神经网络训练目标中。通过对经典校准误差公式引入松弛化处理，我们实现了端到端的反向传播。所提方法不依赖于特定神经网络模型，且相比其引入的收益仅带来适度的计算开销。该方法可直接应用于现有计算流程，实现可靠的黑箱后验推理。在六个基准问题上的实验表明，所提方法在覆盖率和期望后验密度方面达到了与现有方法相当或更优的结果。