Computer model validation with functional output

By Maria J. Bayarri, James O. Berger, John A. Cafeo, G. Garc'ia-Donato, F. Liu, Jesús Palomo, R. Parthasarathy, R. Paulo, J. Sacks, D. Walsh. 2007

323 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/330d789975c35a29b027fdc3c4fc92f45cd77a0e

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Citations in the corpus

Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models (2009, methodology): “[11] use principle components and wavelet decomposition, respectively, to decompose the multiple outputs (possibly even a whole function of values over time and/or space) into just several components which can be considered as independent outputs.”
Predicting Vehicle Crashworthiness: Validation of Computer Models for Functional and Hierarchical Data (2009, methodology): “The methodology from Bayarri et al. (2007b) that we are adopting does not accommodate qualitative inputs such as barrier type.”
A Framework for Validation of Computer Models (2007, methodology): “Two such extensions of the methodology – to functional data – are considered in Bayarri et al. (2005a) and Bayarri et al. (2005b).”
Choosing the Sample Size of a Computer Experiment: A Practical Guide (2009, methodology): “functional output as in Higdon et al. (2005) and Bayarri et al. (2007) .”
Efficient Emulators for Multivariate Deterministic Functions (2008, methodology): “This has been discussed in Kennedy and O’Hagan (2001), Bayarri et al. (2005), and Conti and O’Hagan (2007).”