|
Abstract:
|
Many scientific disciplines use simulations extensively to study complex phenomena. While simulators can generate high-fidelity observable data, they encode the likelihood only implicitly. Classical statistical methods are poorly suited for these likelihood-free inference (LFI) settings, and LFI can be even more challenging for complex high-dimensional data. Research in this area is estimating parameters with a prediction approach, thereby leveraging the flexibility of machine learning algorithms to improve computational times and accuracy in parameter estimation. Nonetheless, it remains an open question whether these tools produce reliable measures of uncertainty. In this work we present Waldo, a novel method to construct frequentist confidence sets in an LFI setting. Waldo reframes the well-known Wald test to convert parameter point estimates from any prediction algorithm to confidence sets that are guaranteed to have the nominal coverage even in finite samples. The LFI framework we exploit allows to check coverage across the entire parameter space. We show the efficacy of Waldo with theoretical and empirical results, and apply it to muon energy estimation in high-energy physics.
|
