Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability

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.