No abstract

We develop a statistical approach for characterizing uncertainty in predictions that are made with the aid of a computer simulation model. Typically, the computer simulation code models a physical system and requires a set of inputs-some known and specified, others unknown. A limited amount of field data from the true physical system is available to inform us about the unknown inputs and also to inform us about the uncertainty that is associated with a simulationbased prediction. The approach given here allows for the following: • uncertainty regarding model inputs (i.e., calibration); • accounting for uncertainty due to limitations on the number of simulations that can be carried out; • discrepancy between the simulation code and the actual physical system; • uncertainty in the observation process that yields the actual field data on the true physical system. The resulting analysis yields predictions and their associated uncertainties while accounting for multiple sources of uncertainty. We use a Bayesian formulation and rely on Gaussian process models to model unknown functions of the model inputs. The estimation is carried out using a Markov chain Monte Carlo method. This methodology is applied to two examples: a charged particle accelerator and a spot welding process.

A key question in evaluation of computer models is Does the computer model adequately represent reality? A six-step process for computer model validation is set out in Bayarri et al. [Technometrics 49 (2007) 138--154] (and briefly summarized below), based on comparison of computer model runs with field data of the process being modeled. The methodology is particularly suited to treating the major issues associated with the validation process: quantifying multiple sources of error and uncertainty in computer models; combining multiple sources of information; and being able to adapt to different, but related scenarios. Two complications that frequently arise in practice are the need to deal with highly irregular functional data and the need to acknowledge and incorporate uncertainty in the inputs. We develop methodology to deal with both complications. A key part of the approach utilizes a wavelet representation of the functional data, applies a hierarchical version of the scalar validation methodology to the wavelet coefficients, and transforms back, to ultimately compare computer model output with field output. The generality of the methodology is only limited by the capability of a combination of computational tools and the appropriateness of decompositions of the sort (wavelets) employed here. The methods and analyses we present are illustrated with a test bed dynamic stress analysis for a particular engineering system.Comment: Published in at http://dx.doi.org/10.1214/009053607000000163 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

No abstract