Efficient Quantification of Uncertainties Associated with Reservoir Performance Simulations Dongxiao Zhang, The University of Oklahoma . The efficiency and accuracy of a stochastic approach to stochastic partial differential equations depend on how the underlying random field and the dependent variables are represented. The following example shows how the random pressure head field is approximated with 1000 independent, equally probable realizations in the direct sampling Monte Carlo method (left) and with 28 representations (with various weights) in the probabilistic collocation method (right), both of which led to almost the same statistics.