A classical statistical model of hypothesis testing is the Blackwell Le Cam experiment, in which an observer makes inferences regarding the veracity of an hypothesis by observing a random outcome whose distribution depends on whether or not the hypothesis holds. We address a number of natural, classical questions: when does one experiment have more information than another? How can we quantify the amount of information an experiment holds? Our results include an answer to an old question of Blackwell, as well as a novel axiomatization of Kullback-Leibler divergence.
Joint with Xiaosheng Mu, Luciano Pomatto and Philipp Strack