  In this paper we study a rational inattention model in environments where the
decision maker faces uncertainty about the true prior distribution over states.
The decision maker seeks to select a stochastic choice rule over a finite set
of alternatives that is robust to prior ambiguity. We fully characterize the
distributional robustness of the rational inattention model in terms of a
tractable concave program. We establish necessary and sufficient conditions to
construct robust consideration sets. Finally, we quantify the impact of prior
uncertainty, by introducing the notion of \emph{Worst-Case Sensitivity}.
