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This paper introduces the “Discrete Direct” (DD) model calibration and uncertainty propagation approach for computational models calibrated to data from sparse replicate tests of stochastically varying systems. The DD approach generates and propagates various discrete realizations of possible calibration parameter values corresponding to possible realizations of the uncertain inputs and outputs of the experiments. This is in contrast to model calibration methods that attempt to assign or infer continuous probability density functions for the calibration parameters-which incorporates unjustified information in the calibration and propagation problem. The DD approach straightforwardly accommodates aleatory variabilities and epistemic uncertainties in system properties and behaviors, in input initial and boundary conditions, and in measurement uncertainties in the experiments.