  The current standard Bayesian approach to model calibration, which assigns a
Gaussian process prior to the discrepancy term, often suffers from issues of
unidentifiability and computational complexity and instability. When the goal
is to quantify uncertainty in physical parameters for extrapolative prediction,
then there is no need to perform inference on the discrepancy term. With this
in mind, we introduce Gibbs posteriors as an alternative Bayesian method for
model calibration, which updates the prior with a loss function connecting the
data to the parameter. The target of inference is the physical parameter value
which minimizes the expected loss. We propose to tune the loss scale of the
Gibbs posterior to maintain nominal frequentist coverage under assumptions of
the form of model discrepancy, and present a bootstrap implementation for
approximating coverage rates. Our approach is highly modular, allowing an
analyst to easily encode a wide variety of such assumptions. Furthermore, we
provide a principled method of combining posteriors calculated from data
subsets. We apply our methods to data from an experiment measuring the material
properties of tantalum.
