objective function, which constitutes some form of the disagreement between the experimental measurements and model predictions, is minimized over a subset of model parameters appropriately selected based on their uncertainty and sensitivity. The second approach to calibration is Bayesian inference, which explicitly acknowledges the uncertainty in the model parameters. In Bayesian inference, calibration is achieved by reducing the uncertainty in the models parameters and in turn reducing the uncertainty in the model output, and it is therefore considered to be more refined than optimization-based procedures. The present manuscript implements a Bayesian implementation of Kennedy and O’Hagan’s method [1]. This implementation, derived from Higdon et al. [2], is built into a computer code called Gaussian Process Model – Simulation Analysis (GPM-SA) at the Los Alamos National Laboratory. It is deeply rooted in the following relation: ǔobs (x) = ysim (x, ș) + δ(x) + ε(x) (1) In Equation (1), the parameter x denotes the control variables. One must be careful not to mix control parameters,x, with calibration parameters, denoted by ș in Equation (1). Control parameters, which can controlled during experiments, define the domain of applicability. Calibration parameters on the other hand are either introduced by specific choices of assumptions or models, or they represent parameters that cannot be measured or controlled experimentally. In Equation (1), ysim(x, ș) corresponds to the model predictions, į(x) corresponds to a discrepancy bias that represents the systematic bias, and İ(x) represents the random experimental error. When these three terms are added together, they yield our best estimate for the “truth”, ǔobs (x) over the various settings of x in the domain of applicability. To reiterate Equation (1), if the discrepancy bias associated with a simulation model is known, the truth, yobs(x) can be computed by correcting model predictions, ysim (x, ș) with the discrepancy bias δ(x). One of the primary roles of experimental measurements is to supply information about the discrepancy bias at discrete points within the domain of applicability. We now introduce another term, xt, which denotes the control parameter settings where the experimental measurements are available. ǔobs (x t) ~ y obs (x t) (2) 434
RkJQdWJsaXNoZXIy MTMzNzEzMQ==