Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification by Validation and Uncertainty Quantification Committee on Mathematical Foundations of Verification

Author:Validation and Uncertainty Quantification Committee on Mathematical Foundations of Verification
Language: eng
Format: azw3
Tags: ebook, book
Published: 2018-09-24T16:00:00+00:00

where e denotes the measurement error. The computer model is exercised at a limited number of input configurations (x,θ), shown by the dots in Figures 5.2.1(a), (b), and (c). Next, an emulator of the computational model can be constructed and used in place of the simulator (Figure 5.2.1(b)). Alternately, the construction of the emulator and estimation of θ can be done jointly using a hierarchical model that specifies, say, a GP model for η( ) and treats the estimation of θ as a missing-data problem. Inferences about the parameter θ, for example, can be made using its posterior probability distribution, usually sampled by means of MCMC (Higdon et al., 2005; Bayarri et al., 2007a).

The physical observations and the computational model can be combined to estimate the parameter θ, thereby constraining the predictions of the computational model. Looking again at Figure 5.2.1(c), the probability density function (PDF) (shown by the solid curve in the center) shows the updated uncertainty for θ after combining the computational model with the physical observations. Clearly, the physical observations have greatly improved the knowledge of the unknown parameter, reducing the prediction uncertainty in the drop time for a bowling-ball drop of 100 m.

Finding: Bayesian methods can be used to estimate parameters and provide companion measures of uncertainty in a broad spectrum of model calibration and inverse problems. Methodological challenges remain in settings that include high-dimensional parameter spaces, expensive forward models, highly nonlinear or even discontinuous forward models, and high-dimensional observables, or in which small probabilities need to be estimated.

Recommendation: Researchers should understand both VVUQ methods and computational modeling to more effectively exploit synergies at their interface. Educational programs, including research programs with graduate-education components, should be designed to foster this understanding.

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