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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 ...
Given some experimental measurements of a system and some computer simulation results from its mathematical model, inverse uncertainty quantification estimates the discrepancy between the experiment and the mathematical model (which is called bias correction), and estimates the values of unknown parameters in the model if there are any (which ...
(Maximum Uncertainty Principle) For any event, if there are multiple reasonable values that an uncertain measure may take, then the value as close to 0.5 as possible is assigned to the event. Uncertain variables
The probability that an uncertain number represented by a p-box D is less than zero is the interval Pr(D < 0) = [F(0), F̅(0)], where F̅(0) is the left bound of the probability box D and F(0) is its right bound, both evaluated at zero. Two uncertain numbers represented by probability boxes may then be compared for numerical magnitude with the ...
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation [ 1 ] for an idealized simple pendulum is, approximately,
Shapley effects rely on Shapley values and represent the average marginal contribution of a given factors across all possible combinations of factors. These value are related to Sobol’s indices as their value falls between the first order Sobol’ effect and the total order effect. [39]
Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.
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.