Collocation algorithms for efficiently solving stochastic dif- ferential equations arising from modeling uncertainty in large-scale systems are presented. The resulting solution s are integrated to compute statistical moments, from which sen- sitivity can be inferred, and interpolated to propagate PDF's. We give a detailed exposition of this approach, focusing on the dimension-adaptive algorithm of (10). We give applica- tions on a double pendulum, an integrated shipboard power system, and a pulse power system.