Computationally efficient uncertainty propagation using the stochastic response surface method with Bayesian parameter estimation techniques
S. Isukapalli, Y. Mun, and P.G. Georgopoulos
Environmental and Occupational Health Sciences Institute, a Joint Institute of UMDNJ-Robert Wood Johnson Medical School and Rutgers, the State University of New Jersey, Piscataway, NJ
The Stochastic Response Surface Method (SRSM) is a recently developed, computationally efficient technique for uncertainty propagation through numerical computational models. The SRSM provides an alternative to traditional techniques such as Monte Carlo and Latin Hypercube Sampling by approximating model outputs as probabilistic response surfaces involving orthogonal polynomials of standard random variables; this approximation is also known as the polynomial chaos expansion. The coefficients of the polynomial approximation are estimated from the model outputs at a set of sample points either via collocation or regression techniques. These coefficients provide combined sensitivity and uncertainty information of model outputs with respect to model inputs. This helps in identifying those inputs that contribute to the output uncertainties the most, thus allowing for prioritizing further studies and data gathering efforts. The application of the SRSM so far has involved prior (a priori) selection of collocation or regression points in order to estimate the polynomial chaos expansion coefficients. The current work presents algorithmic improvements to the SRSM by utilizing Bayesian techniques for estimating the coefficients of polynomial expansion. The improvements to the SRSM are implemented as modules of the MENTOR system (Modeling ENvironment for TOtal Risk studies), and the new SRSM modules are evaluated from the perspective of (a) estimating output uncertainties, (b) assessing contributions of individual input uncertainties, (c) computational efficiency, and (d) ability to utilize outputs from the available model runs. A comparative evaluation of the SRSM with regression and Bayesian techniques is presented for different environmental models with a diverse set of probability distributions for the model inputs including simple mixture distributions.
This work had been funded in part by the US Environmental Protection Agency under Cooperative Agreement # EPAR-827033 to the Environmental and Occupational Health Sciences Institute (EOHSI). The viewpoints expressed here are the responsibility of the authors and do not necessarily reflect the views of the USEPA or its contractors.