Calibration and Uncertainty Analysis of Predictions from Computer Experiments

Computer experiments are simulations of physical experiments performed by exercising a mathematical model for a physical or chemical process, to produce model outputs corresponding to sets of values of inputs to the model. They are especially useful when the corresponding physical experiments are difficult or expensive. In these cases one will perform a relatively small number of physical experiments that are used to calibrate the simulation model. This is then employed to explore the space of values of the inputs extensively, in a way that "interpolates" the results of the physical experiments. Quantification of uncertainty for the outputs of such computer experiments is of great interest. The sources of uncertainty are in part due to the experimental measurement uncertainty in the inputs, and in part due to inadequacies of the underlying mathematical model.

This talk will present calibration and assessment of both types of uncertainty, based on modeling by Gaussian random functions, also called Gaussian stochastic processes. The estimation and prediction is accomplished by Markov Chain Monte Carlo using Bayesian methods and is demonstrated on output from two simple fire models. These are the MQH and Beyler methods for the prediction of Hot Gas Layer Temperature in a room fire. They are calibrated using experimental data from the report Verification and validation of selected fire models for nuclear power plant applications, NUREG-1824, Vols. 1 - 7.