"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Calibrating Environmental Engineering Models and Uncertainty Analysis

David Ruppert, Ph.D., Andrew Schultz Jr., Professor of Industrial Engineering, Cornell University


Friday, September 29, 2008

4:00 p.m. 223 Weber

ABSTRACT

A Bayesian approach is taken to model calibration and uncertainty analysis when evaluation of the model is computationally expensive. In this context, calibration is a nonlinear regression problem: given data vector Y corresponding to the regression
model f(beta), find plausible values of beta, or, more precisely, find the posterior distribution of beta. As an intermediate step, Y and f are embedded into a statistical model allowing non-normal errors, nonconstant variance, and dependence. Typically, this problem is solved by sampling from the posterior distribution of beta given Y using MCMC. To reduce computational cost, we limit evaluation of f to small number of points chosen on a high posterior density region found by optimization. Then, we approximate the log-posterior using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC. We illustrate our approach on simulated data for a pollutant diffusion problem and study frequentist coverage properties of credible intervals. Numerical
experiments indicate that our method can produce results similar to those when the true"expensive'' posterior is sampled by MCMC while reducing computational costs by well over an order of magnitude.