Bayesian statistics for effective field theories
Richard Furnstahl, Ohio State University, USA
The physics of the atomic nucleus gives rise to a tower of emergent phenomena at widely varying energy scales. A method called effective field theory (EFT) turns the challenge of dealing with these disparate scales into an advantage by using their ratios as expansion parameters. But despite the promised systematic nature of this approach, a robust framework to include theoretical uncertainties in EFT predictions of experiment has been lacking. This has changed with the first applications of Bayesian statistics to EFTs. Truncation errors for the EFT expansion of nuclear force predictions in continuous domains (functions of energy and scattering angle) are well accounted for by a discrepancy model using Gaussian processes (GPs). Posteriors for the GP parameters give novel physical insight into the nature of EFT expansions, such as their breakdown scales. Model checking diagnostics are proving to be useful not only to validate credibility intervals but as tools for physics discovery. The first successes motivate future applications using Bayesian model selection and model averaging.