  Transfer learning uses a data model, trained to make predictions or
inferences on data from one population, to make reliable predictions or
inferences on data from another population. Most existing transfer learning
approaches are based on fine-tuning pre-trained neural network models, and fail
to provide crucial uncertainty quantification. We develop a statistical
framework for model predictions based on transfer learning, called RECaST. The
primary mechanism is a Cauchy random effect that recalibrates a source model to
a target population; we mathematically and empirically demonstrate the validity
of our RECaST approach for transfer learning between linear models, in the
sense that prediction sets will achieve their nominal stated coverage, and we
numerically illustrate the method's robustness to asymptotic approximations for
nonlinear models. Whereas many existing techniques are built on particular
source models, RECaST is agnostic to the choice of source model. For example,
our RECaST transfer learning approach can be applied to a continuous or
discrete data model with linear or logistic regression, deep neural network
architectures, etc. Furthermore, RECaST provides uncertainty quantification for
predictions, which is mostly absent in the literature. We examine our method's
performance in a simulation study and in an application to real hospital data.
