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The measure precision at k, for example, is a measure of precision looking only at the top ten (k=10) search results. More sophisticated metrics, such as discounted cumulative gain , take into account each individual ranking, and are more commonly used where this is important.
Uncertainty may be implied by the last significant figure if it is not explicitly expressed. [1] The implied uncertainty is ± the half of the minimum scale at the last significant figure position. For example, if the mass of an object is reported as 3.78 kg without mentioning uncertainty, then ± 0.005 kg measurement uncertainty may be implied.
Quantitative uses of the terms uncertainty and risk are fairly consistent among fields such as probability theory, actuarial science, and information theory. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, surprisal is a variation on uncertainty sometimes used in information theory ...
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 ...
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured ...
For example, a spectrometer fitted with a diffraction grating may be checked by using it to measure the wavelength of the D-lines of the sodium electromagnetic spectrum which are at 600 nm and 589.6 nm. The measurements may be used to determine the number of lines per millimetre of the diffraction grating, which can then be used to measure the ...
Uncertainty quantification (UQ) is the science of quantitative characterization and estimation 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.