A New Form of Jensen's Inequality and its Application to Statistical Experiments
Jensen's inequality for the expectation of a convex function of a random variable is proved for a wide class of convex functions defined on a space of probability measures. The result is applied to statistical experiments using the concept of Blackwell-sufficiency. In particular, we show a monotonicity result for the expected information of Poisson experiments. As an application to economics we consider the introduction of new production technologies.
Journal of the Australian Mathematical Society, Series B