Dear Balraj Singh,

estimating the correlation and partial correlation coefficient is a good tool for sample based uncertainty analysis.

Other statistical methods such as chi-square test, T-test, Q-test,... can be also used.

If the soft computing techniques are used for fault detection purposes, different techniques including confusion matrix (CM), receiver operating characteristic (ROC) and area under the curve(AUC) can be also used to predication performances of soft computing techniques.

good books:

* Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems

Authors: Dan G. Cacuci, Mihaela Ionescu-Bujor, Ionel Michael Navon

https://www.crcpress.com/Sensitivity-and-Uncertainty-Analysis-Volume-II-Applications-to-Large-Scale/Cacuci-Ionescu-Bujor-Navon/p/book/9781584881162

* Pattern Recognition and Classification An Introduction

Authors: Dougherty, Geoff

https://www.springer.com/gp/book/9781461453222

The steps are:

1. Ascertain the sources of possible errors.

2. Carry out your measurements.

3. Estimate the uncertainty of each input parameter e.g. standard error.

4. Make sure the errors are independent of each other e.g. using the Durbin-Watson statistic.

5. Calculate your your result e.g. mean and standard error.

6. Find the combined standard uncertainty e.g. use summation in quadrature (square root of the sum of the squares of the values).

7. Express the uncertainty in terms of a coverage factor (e.g. k = 2) together with a size of the uncertainty interval, and state a level of confidence. Multiply the combined standard uncertainty by k to give an expanded uncertainty, which should provide a 95% level of confidence.

Thanks Ali Chaibakhsh and Andrew Paul McKenzie Pegman

Dear Balraj Singh,

If you are asking about interpolation, the note:

Deleted research item The research item mentioned here has been deleted

it is about an interpolation example for temperaturate data; its uncertainty analysis is based on residuals (deviation for initial data and interpolated data)