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Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if we exactly knew the speed, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in a statistical sense. Many problems in the natural sciences and engineering are also rife with sources of uncertainty. Computer experiments on computer simulations are the most common approach to study problems in uncertainty quantification.〔Jerome Sacks, William J. Welch, Toby J. Mitchell and Henry P. Wynn, ''Design and Analysis of Computer Experiments'', Statistical Science, Vol. 4, No. 4 (Nov., 1989), pp. 409-423〕〔Ronald L. Iman, Jon C. Helton, ''An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models'', Risk Analysis, Volume 8, Issue 1, pages 71–90, March 1988, DOI: 10.1111/j.1539-6924.1988.tb01155.x〕〔W.E. Walker, P. Harremoës, J. Rotmans, J.P. van der Sluijs, M.B.A. van Asselt, P. Janssen and M.P. Krayer von Krauss, ''Defining Uncertainty: A Conceptual Basis for Uncertainty Management in Model-Based Decision Support'', Integrated Assessment, Volume 4, Issue 1, 2003, DOI: 10.1076/iaij.4.1.5.16466〕 ==Sources of uncertainty== Uncertainty can enter mathematical models and experimental measurements in various contexts. One way to categorize the sources of uncertainty is to consider:〔Marc C. Kennedy, Anthony O'Hagan, ''Bayesian calibration of computer models'', Journal of the Royal Statistical Society, Series B Volume 63, Issue 3, pages 425–464, 2001〕 * Parameter uncertainty, which comes from the model parameters that are inputs to the computer model (mathematical model) but whose exact values are unknown to experimentalists and cannot be controlled in physical experiments, or whose values cannot be exactly inferred by statistical methods. Examples are the local free-fall acceleration in a falling object experiment, various material properties in a finite element analysis for engineering, and multiplier uncertainty in the context of macroeconomic policy optimization. * Parametric variability, which comes from the variability of input variables of the model. For example, the dimensions of a work piece in a process of manufacture may not be exactly as designed and instructed, which would cause variability in its performance. * Structural uncertainty, aka model inadequacy, model bias, or model discrepancy, which comes from the lack of knowledge of the underlying true physics. It depends on how accurately a mathematical model describes the true system for a real-life situation, considering the fact that models are almost always only approximations to reality. One example is when modeling the process of a falling object using the free-fall model; the model itself is inaccurate since there always exists air friction. In this case, even if there is no unknown parameter in the model, a discrepancy is still expected between the model and true physics. * Algorithmic uncertainty, aka numerical uncertainty, which comes from numerical errors and numerical approximations per implementation of the computer model. Most models are too complicated to solve exactly. For example, the finite element method or finite difference method may be used to approximate the solution of a partial differential equation, which, however, introduces numerical errors. Other examples are numerical integration and infinite sum truncation that are necessary approximations in numerical implementation. * Experimental uncertainty, aka observation error, which comes from the variability of experimental measurements. The experimental uncertainty is inevitable and can be noticed by repeating a measurement for many times using exactly the same settings for all inputs/variables. * Interpolation uncertainty, which comes from a lack of available data collected from computer model simulations and/or experimental measurements. For other input settings that don't have simulation data or experimental measurements, one must interpolate or extrapolate in order to predict the corresponding responses. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Uncertainty quantification」の詳細全文を読む スポンサード リンク
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