  In prediction problems, it is common to model the data-generating process and
then use a model-based procedure, such as a Bayesian predictive distribution,
to quantify uncertainty about the next observation. However, if the posited
model is misspecified, then its predictions may not be calibrated -- that is,
the predictive distribution's quantiles may not be nominal frequentist
prediction upper limits, even asymptotically. Rather than abandoning the
comfort of a model-based formulation for a more complicated non-model-based
approach, here we propose a strategy in which the data itself helps determine
if the assumed model-based solution should be adjusted to account for model
misspecification. This is achieved through a generalized Bayes formulation
where a learning rate parameter is tuned, via the proposed generalized
predictive calibration (GPrC) algorithm, to make the predictive distribution
calibrated, even under model misspecification. Extensive numerical experiments
are presented, under a variety of settings, demonstrating the proposed GPrC
algorithm's validity, efficiency, and robustness.
