Validating quantitative data model

The assessment of these two forecast methods is relatively straightforward because of the large number of comparisons of model forecast to measurement. while most practitioners recognize that this concept and notion are important, rigorous mathematical definitions and quantifications remain an unsolved problem.In some validation applications, an opportunity exists to carry out additional experiments to improve the prediction uncertainty and/or the reliability of the prediction.In some cases these data are observational, provided by nature (e.g., meteorological measurements, supernova luminosities); in other cases, data come from a carefully planned hierarchy of controlled experiments—e.g., the Predictive Engineering and Computational Sciences (PECOS) case study in Section 5.9.In addition to physical observations, information may come from the literature or expert judgment that may incorporate historical data or known physical behavior.The top histogram shows residuals from the persistence model, predicting tomorrow’s high temperature with today’s high temperature.

However, FIGURE 5.1 Daily maximum temperatures for Norman, Oklahoma (left), and histograms of next-day prediction errors (right) using two prediction models.This more complicated formulation can also produce predictions for system behavior in new domains where no physical observations are available (see Bayarri et al., 2007a; Wang et al., 2009; or the case studies of this chapter).Assessing prediction uncertainty is crucial for both validation (which involves comparison with measured data) and prediction of yet-unmeasured QOIs.In simple settings validation could be accomplished by directly comparing model results to physical measurements for the QOI and computing a confidence interval for the difference, or carrying out a hypothesis test of whether or not the difference is greater than the tolerance (see Oberkampf and Roy, 2010, Chapter 12).In other settings, a more complicated statistical modeling formulation may be required to combine simulation output, various kinds of physical observations, and expert judgment to produce a prediction with accompanying prediction uncertainty, which can then be used for the assessment.

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