Matthew Pratola - PhD Defence
Development in Computer Model Calibration
Computer models enable scientists to investigate real-world phenomena virtually using computer experiments. Recently, statistical calibration enabled scientists to incorporate field data and estimate unknown physical constants. In this thesis, we outline three new developments for the statistical calibration of computer models.
The first development is a practical approach for calibrating large and non-stationary computer model output. We present a new computationally efficient approach using a criterion that measures the discrepancy between the computer model and field data. One can then construct empirical distributions for the parameters and sequentially add design points to improve these estimates. The strength of this approach is its simple computation using existing algorithms. Our method also provides good parameter estimates for large and non-stationary data.
The second development deals with incorporating derivative information from the computer model into a calibration experiment. Many computer models are governed by differential equations, and including this derivative information can be helpful. Although incorporating such information has garnered a lot of attention in some areas of statistics, such as penalized regression, it has been largely ignored in computer experiments. We develop a new statistical methodology for the calibration of a computer model when derivative information is additionally available.
The final development deals with extending the methodology incorporating derivatives to allow for the inclusion of possible bias in the computer model. A statistical model accounting for such bias was previously proposed, but heavily criticised as not being identifiable. We develop a model that accounts for this possible bias while simultaneously including the derivative information from the computer model in the hopes that such identifiability issues can be reduced or eliminated. Our results indicate some modest improvements over the previous approach in some experimental conditions. Proving exact conditions where such models can be identified remains interesting and challenging research to explore in future work.
Keywords: Calibration Parameter Estimation; Gaussian Process; Sequential Design; Derivative Information; Bayesian Modelling; Kriging