  We present procedures based on Bayesian statistics for estimating, from data,
the parameters of effective field theories (EFTs). The extraction of low-energy
constants (LECs) is guided by theoretical expectations in a quantifiable way
through the specification of Bayesian priors. A prior for natural-sized LECs
reduces the possibility of overfitting, and leads to a consistent accounting of
different sources of uncertainty. A set of diagnostic tools are developed that
analyze the fit and ensure that the priors do not bias the EFT parameter
estimation. The procedures are illustrated using representative model problems,
including the extraction of LECs for the nucleon mass expansion in SU(2) chiral
perturbation theory from synthetic lattice data.
