STATISTICS COLLOQUIUM
Mengyang Gu
Assistant Research Professor
Department of Applied Mathematics & Statistics
Johns Hopkins University
Calibration of imperfect mathematical models by multiple sources of
data with measurement bias
Abstract
Model calibration involves using experimental or field data to estimate the unknown parameters of a mathematical model. This task is complicated by discrepancy between the model and reality, and by possible bias in field data. We consider model calibration in the presence of both model discrepancy and measurement bias using multiple sources of data. Model discrepancy is often estimated using a Gaussian stochastic process (GaSP), but it was observed in many studies that the calibrated mathematical model can be far from the reality. Here we show that modeling the discrepancy function via a GaSP often leads to an inconsistent estimation of the calibration parameters even if one has an infinite number of repeated experiments and infinite number of observations in each experiment. We introduce the scaled Gaussian stochastic process (S-GaSP) to model the discrepancy function. We establish the explicit connection between the GaSP and S-GaSP through the orthogonal series representation. We show the predictive mean estimator in the S-GaSP calibration model converges to the reality at the same rate as the GaSP with the suitable choice of the regularization parameter and scaling parameter. We also show the calibrated mathematical model in the S-GaSP calibration converges to the one that minimizes the L2 loss between the reality and mathematical model with the same regularization and scaling parameters, whereas the GaSP model does not have this property.
The scientific goal of this work is to use multiple radar satellite interferograms to calibrate a geophysical model of Kilauea Volcano, Hawai`i. We investigate the use of models calibrated using all the data sets simultaneously, and also using stacks (averages) -- a commonly-used approach in geoscience research. The connection and difference between these two approaches are studied. We derive distributions for the maximum likelihood estimator and Bayesian inference, both implemented in the ``RobustCalibration" package available on CRAN. Analysis of both simulated and real data confirm that our approach can identify the measurement bias and model discrepancy using multiple sources of data.
DATE: Wednesday, November 7, 2018
TIME: 4:00 pm
PLACE: Philip E. Austin Bldg., Rm. 108
Coffee will be served at 3:30 pm in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu