We study learning and information acquisition by a Bayesian agent who is misspecified in the sense that his prior belief assigns probability zero to the true state of the world. In our model, at each instant the agent takes an action and observes the corresponding payoff, which is the sum of the...

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990)...