  Conformal prediction is a method of producing prediction sets that can be
applied on top of a wide range of prediction algorithms. The method has a
guaranteed coverage probability under the standard IID assumption regardless of
whether the assumptions (often considerably more restrictive) of the underlying
algorithm are satisfied. However, for the method to be really useful it is
desirable that in the case where the assumptions of the underlying algorithm
are satisfied, the conformal predictor loses little in efficiency as compared
with the underlying algorithm (whereas being a conformal predictor, it has the
stronger guarantee of validity). In this paper we explore the degree to which
this additional requirement of efficiency is satisfied in the case of Bayesian
ridge regression; we find that asymptotically conformal prediction sets differ
little from ridge regression prediction intervals when the standard Bayesian
assumptions are satisfied.
