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.