https://icme.hpc.msstate.edu/mediawiki/index.php/Uncertainty_Quantification_and_Sensitivity_Analysis_Tool

Article A guide to uncertainty quantification and sensitivity analys...

Although not everyone will agree, I distinguish them roughly as follows: a sensitivity analysis concerns the variance of a quantity while an uncertainty quantification concerns the error in that quantity.

Consider a function Y of a random variable X; Y=Y(X). A sensitivity analysis might measure the variance of Y as a function of the variance in X. An uncertainty quantification might determine the root mean squared error (RMSE) in Y due to errors in X. The latter would require a known "true value" (or possibly design value) of Y, likely given by Y(x0) where x0 is the known true value (or design value) of X. Typically, one assigns a probability distribution to X in order to compute the RMSE of Y.

That said, there are a wide variety of opinions as to what constitutes an uncertainty quantification. Just defining uncertainty itself provides a topic that committee members debate for years.

I agree with Gregory that 'a sensitivity analysis concerns the variance of a quantity while an uncertainty quantification concerns the error in that quantity' :)

Dear Dr Sarah Bellil@

I think the following papers

https://qeconomics.org/ojs/forth/866/866-2.pdf

&

https://icme.hpc.msstate.edu/mediawiki/index.php/Uncertainty_Quantification_and_Sensitivity_Analysis_Tool

&

http://www4.ncsu.edu/~rsmith/FSU_SHORT_COURSE17/FSU_Short_Course17.pdf

&

https://www.sciencedirect.com/science/article/pii/S1364815216308088

&

Article A guide to uncertainty quantification and sensitivity analys...

&

https://en.wikipedia.org/wiki/Sensitivity_analysis

are very useful to your question.

With Best Wishes.@@

Both analyses - uncertainty quantification (UQ) and sensitivity analysis (SA) - are essential parts of modeling processes.

- The uncertainty quantification is a mathematical approach that evaluates the uncertainty of model output(s) based on uncertainties of model inputs. UQ deals with identifying the sources of uncertainty and including them in the model, assessing the uncertainty for each model input and propagating them through the model in uncertainty of the model output.

- The sensitivity analysis studies the contribution of uncertainty of each model input to the uncertainty of the model output and identifies dominant contributors.

In the following, I will refer to applying the two types of analysis in metrology, a field in which measurement uncertainty is an essential parameter.

For metrologists, UQ is the evaluating the uncertainty of the result of a measurement, y. If y is not measured directly, but it is calculated from the values ​​of other quantities, values ​​to be further denoted by xi, i = 1, 2, ..., N, it is necessary first to establish the mathematical model of measurement:

y = f (x1, x2, ..., xN). (1)

The uncertainty of y, u(y), can be calculated starting from Eq.(1) and using the law of propagation of uncertainty (GUM). For the simplest case where the input quantities are uncorrelated (see Eq.(10) of the GUM), u(y) results from:

u2(y) = (df /dx1)2 u2(x1) + (df /dx2)2 u2(x2) + ... + (df/dxN)2 u2(xN) (2)

where u(xi) are the uncertainties associated with the input estimates xi, and the derivatives (df/dxi) are called sensitivity coefficients. The uncertainty quantification is the calculation of u(y) using Eq.(2).

In the usual approaches, SA is derivative based and it analyzes the impact of an input in the mathematical model on the model output, keeping the other input parameters fixed.

In the case discussed here, the same Eq.(2) above is the basis of the sensitivity analysis. It refers to determining the variation in y produced by the uncertainty u(xi) of one of the input estimates xi while the other input estimates ​​are considered to be constant. As it follows from Eq.(2), the influence of u(xi) on u(y) is described by the sensitivity coefficients (df/dxi) of Eq.(2), so that the change of y generated by the uncertainty u(xi) is given by

ui(y) = (df/dxi) u(xi), i = 1, 2, ..., N. (3)

Eq.(3) is the sensitivity analysis for the case presented.

In this paper

Article Sensitivity analysis of combined standard uncertainties eval...

you can find methods for uncertainty quantification and sensitivity analysis for a SPRTs calibration model at defining fixed points of the ITS-90.

Good Advice!!!

Hello!

Thank you so much for your answers.

Here an attempt to answer without formulas or a link to an article :)

We get the sensitivity analysis by perturbing an input and measure its effect on the output. The difference with UQ here is:

• first, in sensitivity analysis we consider the input parameters as independent and possible interactions between parameters are not considered.
• Seconds the input perturbation itself is the same for all parameters and does not obey any PDF. Sensitivity analysis is then merely a way to qualitatively rank different parameters based on their effect on the output.

Please see p.352 of

Zheng, C., and G. D. Bennett, Applied Contaminant Transport Modeling, Second Edition, Wiley, New York, 2002.

Sensitivity analysis (SA) is the study of how the uncertainty in model output can be apportioned to different sources of uncertainty in the model input.

Uncertainty quantification (UQ) is the study of how uncertain is the model output and input.

UQ is divided into forward uncertainty quantification and inverse uncertainty quantification.

Forward UQ: propagate uncertainties to put errors bars on model output, which addresses the question "How uncertain is the model output".

Inverse UQ: characterize model input (e.g., model parameter) uncertainty from observations, which addresses the question "How uncertain is the model input".