Recent developments in applying Bayesian statistics to effective field theories

Uncertainty quantification (UQ) is an essential part and one of the main advantages of applying effective field theories (EFT) to low-energy nuclear physics. A Bayesian statistical framework is particularly well suited for this task, as EFT expectations regarding naturalness and truncation errors can be encoded through prior probability distribution functions (PDFs).  The specification of priors means that all theoretical assumptions are explicit in the calculation of the posterior PDFs, making such an analysis reproducible. The BUQEYE collaboration (``Bayesian Uncertainty Quantification: Errors for Your EFT'') has the overall goal of full UQ and associated diagnostics for EFT predictions using Bayesian statistics. This includes parameter estimation, uncertainty propagation to observables, model checking (``Is the EFT and our model for errors working?''), model selection (``Is one EFT implementation better than another?''), and the use of Bayesian statistical methods as a physics diagnostic tool. We will give background and selected results from recent and ongoing work by the BUQEYEs.