The dual quermassintegrals of a star body are defined as the average volume of sections of the body by hyperplanes of fixed dimension. These quantities, along with general dual mixed volumes, see striking parallels with their counterparts in Brunn-Minkowksi theory, especially for their respective extremal inequalities. In this talk, we show how empirical methods provide a way to establish dual inequalities which are based on new local stochastic features within dual Brunn-Minkowski theory. Joint work with G. Paouris and P. Pivovarov.