  We present a new Bayesian approach to model-robust linear regression that
leads to uncertainty estimates with the same robustness properties as the
Huber--White sandwich estimator. The sandwich estimator is known to provide
asymptotically correct frequentist inference, even when standard modeling
assumptions such as linearity and homoscedasticity in the data-generating
mechanism are violated. Our derivation provides a compelling Bayesian
justification for using this simple and popular tool, and it also clarifies
what is being estimated when the data-generating mechanism is not linear. We
demonstrate the applicability of our approach using a simulation study and
health care cost data from an evaluation of the Washington State Basic Health
Plan.
