| Author | Message | ||
     Forrest Stout (forrest) Intermediate Member Username: forrest Post Number: 19 Registered: 7-2006 |
Dongsheng, I would also suggest Chemom. Intell. Lab. Syst. 60 (2002) 173-188 ("Graphical diagnostics for regression model determinations with consideration of the bias/variance trade-off") and J. Chemom. 18 (2004) 372-384 (primarily a ridge regression paper, but it deals with variance, using equations from the paper Dr. Faber just cited). These may help give you a feel for realizing variance in model selection. | ||
| Klaas Faber (faber) New member Username: faber Post Number: 2 Registered: 9-2003 |
Dear Dongsheng, I have to dissapoint you a little bit. There are only technical papers about the connections between figures and merit and uncertainty estimation. [Your immediate question: Do you have educational level materials on mathematical estimation multivariate calibration uncertainty from wavelength/intensity uncertainty, reference measurement uncertainty and overlapped bands? This is detailed in, among others, K. Faber and B.R. Kowalski, "Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares", Journal of Chemometrics, 11 (1997) 181-238. This stuff is, however, hardly educational, see page range!] We recently published this IUPAC report that is pretty up to date on the subject, but it is a review - it doesn't explain too much. I give special courses on the subject. These courses also pay attention on model assumptions. It's not like the usual "black box" modeling we do that only requires predictors (X) and a response (y) and "everything is estimated from the data". Correct uncertainty estimation also requires (possibly independent) uncertainty estimates. Depending on the prior knowledge about the uncertainties in X and/or y, you can get a better validation, outlier detection and even a better model. Hope this helps but I'm not sure! Klaas | ||
| Dongsheng Bu (dbu) Junior Member Username: dbu Post Number: 6 Registered: 6-2006 |
Dear Klaas, I learned a lot from your article "Estimation of prediction uncertainty" at http://www.spectroscopyeurope.com/chemo_16_1.pdf. Estimation of prediction uncertainty seems not difficult to understand from the article and some documents like ASTM_D6122. Could you provide more information on Uncertainty estimation and figures of merit for multivariate calibration? Such as ASTM/USP guidance documents, popular used statistic parameters and how to use those parameters. RMSEC/RMSEP/Bias/Hotelling T2 and Limits are already available in PLS and PCR, plus ANOVA in MLR in the Unscrambler. Do you have educational level materials on mathematical estimation multivariate calibration uncertainty from wavelength/intensity uncertainty, reference measurement uncertainty and overlapped bands? Thanks, Dongsheng | ||
| Klaas Faber (faber) New member Username: faber Post Number: 1 Registered: 9-2003 |
Dear all: From time to time questions are asked that are related to uncertainty estimation. On my website (http://www.chemometry.com/)I have made research available that deals with estimating the uncertainty in results obtained from chemometric models like partial least squares (PLS) regression. A list of researchers that have contributed can be found at: http://www.chemometry.com/Index/Acknowledgements.html As an illustration: Recently, a IUPAC report has been published that reviews uncertainty estimation and analytical figures of merit (e.g. limit of detection) for multivariate calibration. This Part 3 in a series can be downloaded from: http://www.chemometry.com/Index/Calibration.html It deals with progress made over the last 25 years in chemometrics and shows in particular what can be achieved if the data are only partially selective. Think of overlap in chromatography or spectroscopy. NIR is just one of many instrumental techniques to which the methodology covered in that review applies. Basically, much of what is generally accepted for the univariate straight-line fit has been consistently generalized to chemometric multivariate methods like PLS. Unfortunately, very little of this progress has found its way into chemometrics software. Sincerely, Klaas Faber _______________________________ N.M. Faber, Ph.D. Chemometry Consultancy Rubensstraat 7 6717 VD Ede The Netherlands T +31 (0)318 641985 E [email protected] I www.chemometry.com _______________________________ |