Trustworthy Scientific Inference from Limited or Sparse Calibration Data

This talk concerns statistical inference on the internal parameters of complex physical systems, where the likelihood is intractable but encoded by a simulator or in observations of Nature itself. In this so-called likelihood-free inference (LFI) setting, one can estimate key quantities such as likelihoods, posteriors, or likelihood ratios from labeled (e.g. simulated) data. An open question is how to best construct confidence sets with high power for realistic settings with finite sample sizes and model misspecifications. In this work, we leverage estimated posteriors to construct sets with frequentist coverage and high constraining power (small average size) that are robust to several forms of model misspecification and can be estimated using limited or sparse calibration data.

Likelihood-free inference

Model misspecification

Limited data