Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems

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Abstract
Comprehensive uncertainty analyses of complex models of environmental and biological systems are essential but often not feasible due to the computational resources they require. “Traditional” methods, such as standard Monte Carlo and Latin Hypercube Sampling, for propagating uncertainty and developing probability densities of model outputs, may in fact require performing a prohibitive number of model simulations. An alternative is offered, for a wide range of problems, by the computationally efficient “Stochastic Response Surface Methods (SRSMs)” for uncertainty propagation. These methods extend the classical response surface methodology to systems with stochastic inputs and outputs. This is accomplished by approximating both inputs and outputs of the uncertain system through stochastic series of “well behaved” standard random variables; the series expansions of the outputs contain unknown coefficients which are calculated by a method that uses the results of a limited number of model simulations. Two case studies are presented here involving (a) a physiologically‐based pharmacokinetic (PBPK) model for perchloroethylene (PERC) for humans, and (b) an atmospheric photochemical model, the Reactive Plume Model (RPM‐IV). The results obtained agree closely with those of traditional Monte Carlo and Latin Hypercube Sampling methods, while significantly reducing the required number of model simulations.