  Folding uncertainty in theoretical models into Bayesian parameter estimation
is necessary in order to make reliable inferences. A general means of achieving
this is by marginalizing over model uncertainty using a prior distribution
constructed using Gaussian process regression (GPR). As an example, we apply
this technique to the measurement of chirp mass using (simulated)
gravitational-wave signals from binary black holes that could be observed using
advanced-era gravitational-wave detectors. Unless properly accounted for,
uncertainty in the gravitational-wave templates could be the dominant source of
error in studies of these systems. We explain our approach in detail and
provide proofs of various features of the method, including the limiting
behavior for high signal-to-noise, where systematic model uncertainties
dominate over noise errors. We find that the marginalized likelihood
constructed via GPR offers a significant improvement in parameter estimation
over the standard, uncorrected likelihood both in our simple one-dimensional
study, and theoretically in general. We also examine the dependence of the
method on the size of training set used in the GPR; on the form of covariance
function adopted for the GPR, and on changes to the detector noise power
spectral density.
