Uncertainty Analysis for Computationally Expensive Models with Multiple Outputs

• Activity Number: 218
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): David Ruppert*+ and Christine Ann Shoemaker and Yilun Wang and Nikolay Bliznyuk and Yingxing Li
• Companies: Cornell University and Cornell University and Cornell University and University of Florida and Xiamen University
• Keywords: MCMC ; Watershed modeling ; meta-model ; GRIMA algorithm

Abstract

Bayesian MCMC calibration and uncertainty analysis for computationally expensive models is implemented using a radial basis function interpolator, also known as an emulator or meta-model, for the logarithm of the posterior density. The meta-model is a radial basis function interpolator. To prevent wasteful evaluations of the expensive model, the emulator is built only on a high posterior density region (HPDR) located by a global optimization algorithm. The set of points in the HPDR where the expensive model is evaluated is determined sequentially by the GRIMA algorithm developed by the authors. Enhancements of the GRIMA algorithm are introduced to improve efficiency. A case study uses an eight-parameter SWAT (Soil and Water Assessment Tool) model where daily stream flows and phosphorus concentrations are modeled for the Town Brook watershed, a part of the New York City water supply. An interesting feature of this example is that the posterior is bimodal. The HPDR comprises less than 1% (by volume) of the parameter space, so the GRIMA algorithm is much more efficient on this problem than previously available methods.