Following Kamenica and Gentzkow, this paper studies persuasion as an information design problem. We investigate how mistakes in probabilistic inference impact optimal persuasion. The concavification method is shown to extend naturally to a large class of belief updating rules, which we identify and characterize. This class comprises many non-Bayesian models discussed in the literature. We apply this new technique to gain insight into the revelation principle, the ranking of updating rules, when persuasion is beneficial to the sender, and when it is detrimental to the receiver. Our key result also extends to shed light on the question of robust persuasion.