This paper examines the implications of a binary action, binary outcome decision problem for estimating risk. We use data on the invasiveness of biological imports to develop the first comparison of two classical methods—maximum likelihood and Bayesian—against a third, the recently developed maximum utility (MU) approach. MU estimation uniquely takes advantage of the structure of the decision problem, which depends on a local rather than global fit to the model. Extending methods to account for an endogenously stratified sample, we show that the MU approach is less sensitive to specification error and can offer significant economic gains under model uncertainty.