The decision maker is assumed to observe a large number of experiments. The paper presents conditions for the existence of a unique prior over distributions that generate each of the observed samples. The axioms over experiments admit a recursive non-expected utility representation over two-stage lotteries (Klibanoff et al., 2005). This representation allows for preferences that exhibit "ambiguity'' (or "uncertainty'') aversion in a way that is analogous to risk aversion without contravening the time-neutrality axiom of Segal (1990). The paper illustrates the concepts by measuring the relationship between a player's batting average and their salary in Major League Baseball. An increase in a standard measure of uncertainty, the variance of the posterior, is associated with a substantial reduction in player salaries holding other factors fixed.