Daniel Philips (Ohio University)

Bayesian Uncertainty Quantification: Errors for Your EFT

In this talk I will outline a program that uses Bayesian methods to quantify theoretical uncertainties. Effective field theories (EFTs) provide fertile ground for such an effort, since they are defined with a small expansion parameter that can be used to assess the impact of omitted terms on observables. I will first describe our adaptation of a procedure developed for perturbative QCD to the EFT context. This procedure employs information on the convergence of the EFT series to refine a priori expectations regarding the error that results from performing a finite-order EFT calculation. This updating is encoded by Bayes theorem, and the result is a truncation error that can be interpreted in a rigorous (Bayesian) statistical way. I will then move on to talk about how Bayesian methods also improve the extraction of EFT parameters—commonly termed low-energy constants (LECs)—from data. I will show within the context of model problems that Bayesian priors which incorporate the expectation of natural-sized LECs reduce the risk of overfitting, and mean the LEC extraction accounts for both truncation and experimental error. I will also display some of the diagnostic tools our collaboration has developed to ensure that these priors do not bias the EFT parameter estimation. I will close by briefly mentioning some ongoing BUQEYE projects, e.g. the use of Bayesian evidence ratios to test different EFT power counting proposals. While some of my examples will be drawn from EFTs developed for nuclear physics, the set of tools described in the talk should be applicable in many EFT contexts.