  The robustness to the prior of Bayesian inference procedures based on a
measure of statistical evidence are considered. These inferences are shown to
have optimal properties with respect to robustness. Furthermore, a connection
between robustness and prior-data conflict is established. In particular, the
inferences are shown to be effectively robust when the choice of prior does not
lead to prior-data conflict. When there is prior-data conflict, however,
robustness may fail to hold.
