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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Experimental uncertainty analysis is a technique that analyses a derived quantity, based on the uncertainties in the experimentally measured quantities that are used in some form of mathematical relationship ("model") to calculate that derived quantity.
While uncertainty analysis aims to describe the distribution of the output (providing its statistics, moments, pdf, cdf,...), sensitivity analysis aims to measure and quantify the impact of each input or a group of inputs on the variability of the output (by calculating the corresponding sensitivity indices). Figure 1 provides a schematic ...
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Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement.An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on.
The convolution of a function with a Gaussian is also known as a Weierstrass transform. A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
Uncertainty propagation is the quantification of uncertainties in system output(s) propagated from uncertain inputs. It focuses on the influence on the outputs from the parametric variability listed in the sources of uncertainty. The targets of uncertainty propagation analysis can be: