Estimation of low-energy constants (LECs) is an important component of effective field theory (EFT) programs. For low-energy QCD, a direct calculation of LECs from the underlying theory is possible in only a very few cases, and in practice the LECs are determined by fits to experimental data. There are several questions that need to be considered regarding such a fit: How does one incorporate the information that the LECs are of natural size? At which order in the EFT expansion should the fit be performed? And which data should be used to determine the LECs? We propose a method to address these questions that is based on Bayesian probability theory. The Bayesian framework not only allows for a more stable extraction of parameters from data, but also for a more systematic treatment of uncertainties. To demonstrate our method we present the application to a ``toy'' problem as well as a problem in chiral perturbation theory.
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