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A recent performance assessment for the Waste Isolation Pilot Plant (WIPP), which is being developed by the U.S. Department of Energy for the geologic disposal of transuranic waste, is used to illustrate the computational structure of a large analysis that maintains a separation between stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty. In this analysis, stochastic uncertainty arises from the many possible disruptions that could occur over the 10,000 yr regulatory period that applies to the WIPP, and subjective uncertainty arises from the imprecision with which many of the quantities required in the analysis are known. Important parts of the computational structure are (1) the use of Latin hyper cube sampling to incorporate the effects of subjective uncertainty, (2) the use of Monte Carlo (i.e., random) sampling to incorporate the effects of stochastic uncertainty, and (3) the efficient use of the necessarily limited number of mechanistic calculations that can be performed to support the analysis.