Control of modeling error in calibration and validation processes for predictive stochastic models

Our view of how computer modeling and simulation impact the world of science and engineering has evolved in recent years to one in which the principal factors affecting predictability of a simulation and their interaction with one another are more clearly distinguishable than ever before. Among these factors are (1) the selection of a mathematical model that provides an abstraction of the physical events of interest; (2) the identification of appropriate parameters that define the model; (3) the use of physical observations and measurements to calibrate and validate the model; (4) the development of a computational model through discretization of the mathematical model; (5) the identification of the specific goals of the simulation, the quantities of interest or target outputs; and (6) the quantification of the uncertainty in the predictions. An obvious property of each of these factors is that they all are imprecise and lead to error and uncertainty in predictions: the heuristic act of selecting a mathematical abstraction of physical reality can be the most critical source of error, which we call modeling error; the parameters of the model are rarely known precisely and can generally be determined only in some rough statistical sense, and the same is true of observations and measurements that are obtained through imperfect systems and devices and which are generally limited to only a few features of the response of the system; the corruption of the model due to discretization leads to discretization (or ‘numerical’) error, and all these errors propagate through the target outputs, which represent quantities with significant uncertainty.