Search results
Results from the WOW.Com Content Network
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 real life applications, both kinds of uncertainties are present. Uncertainty quantification intends to explicitly express both types of uncertainty separately. The quantification for the aleatoric uncertainties can be relatively straightforward, where traditional (frequentist) probability is the most basic form.
This statistics -related article is a stub. You can help Wikipedia by expanding it.
Figure 1. Schematic representation of uncertainty analysis and sensitivity analysis. In mathematical modeling, uncertainty arises from a variety of sources - errors in input data, parameter estimation and approximation procedure, underlying hypothesis, choice of model, alternative model structures and so on.
4. The solution is to expand the function z in a second-order Taylor series; the expansion is done around the mean values of the several variables x. (Usually the expansion is done to first order; the second-order terms are needed to find the bias in the mean. Those second-order terms are usually dropped when finding the variance; see below). 5.
Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions.
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.
If the data exhibit a trend, the regression model is likely incorrect; for example, the true function may be a quadratic or higher order polynomial. If they are random, or have no trend, but "fan out" - they exhibit a phenomenon called heteroscedasticity. If all of the residuals are equal, or do not fan out, they exhibit homoscedasticity.