  Bayesian procedures designed to quantify truncation errors in perturbative
calculations of quantum chromodynamics observables are adapted to expansions in
effective field theory (EFT). In the Bayesian approach, such truncation errors
are derived from degree-of-belief (DOB) intervals for EFT predictions.
Computation of these intervals requires specification of prior probability
distributions ("priors") for the expansion coefficients. By encoding
expectations about the naturalness of these coefficients, this framework
provides a statistical interpretation of the standard EFT procedure where
truncation errors are estimated using the order-by-order convergence of the
expansion. It also permits exploration of the ways in which such error bars
are, and are not, sensitive to assumptions about EFT-coefficient naturalness.
We first demonstrate the calculation of Bayesian probability distributions for
the EFT truncation error in some representative examples, and then focus on the
application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and
Mei{\ss}ner recently articulated explicit rules for estimating truncation
errors in such EFT calculations of few-nucleon-system properties. We find that
their basic procedure emerges generically from one class of naturalness priors
considered, and that all such priors result in consistent quantitative
predictions for 68% DOB intervals. We then explore several methods by which the
convergence properties of the EFT for a set of observables may be used to check
the statistical consistency of the EFT expansion parameter.
