Attacking Parameter Uncertainty in Calibration Problems Arising in Environmental Engineering

Stefan Wild, Cornell University

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The calibration of complex modeling systems is a recurring problem in almost any engineering discipline. Researchers often have a computationally expensive model (simulator) of an underlying physical process which relies on a set of parameters, P, as well as data generated by Nature, presumably according to this model for some (unknown) value of these parameters. Calibration asks, for what value of P does the model most closely resemble available data? This problem is complicated when the presence of measurement error and other noise often leads to uncertainty in the estimated parameters.

Practitioners often have some idea of the magnitude of the unknown parameters, suggesting a Bayesian approach which takes into account both the practitioner’s prior beliefs and the relationship between the data and the model. The standard approach is to then obtain marginal posterior distributions for each of the model parameters using MCMC sampling.

In practice, this approach is infeasible because of the computational bottleneck of evaluating the computationally-expensive model at many different parameter values. We utilize a surrogate model to approximate the true model in the “most important” areas of the parameter space. Sampling from this computationally-inexpensive surrogate then yields high-quality approximations of the desired posterior distributions.

We provide initial results from the application of this procedure to some synthetic problems arising in Environmental Engineering.

Abstract Author(s): Nikolai Blizniouk, David Ruppert, Christine Shoemaker, Stefan Wild