Number: 2004-041-1-500
Title: Uncertainty estimation and figures of merit for multivariate
calibration
Task Group
Chairman: Alejandro
C. Olivieri
Members: Ricard Boqué,
Nicholaas (Klaas) M. Faber,
Joan Ferré, John
H. Kalivas, and Howard
Mark
Completion Date: 2006 - project completed
Objective:
To provide chemists in general, and analytical chemists in particular,
with an introduction to uncertainty propagation and figures of merit
in multivariate calibration from a chemometrics perspective, and to
review the various proposals to generalizing the well-established univariate
methodology to the multivariate domain.
The work is intended as a continuation (i.e., Part 3) of the IUPAC
series of Technical Reports "Guidelines for calibration in analytical
chemistry", Part 1, Fundamentals and single component calibration,
Pure Appl. Chem.
1998, 70, 993-1014, and Part 2, Multispecies calibration,
Pure Appl.
Chem.
2004, 76, 1215-1225.
Description:
With the ever-increasing sophistication of analytical instruments, multivariate
calibration methods are continually evolving, each with its own underlying
assumptions and statistical properties. The main purpose of these methods
is to produce valid predictions from highly unselective data, e.g. the
quantification from near-infrared spectra. A wide variety of multivariate
methods have been developed, broadly classified in terms of the tensorial
order of the instrumental data. Important conceptual differences exist
between first-order methods employing vector data, and second-order
methods using matrix data, particularly since the latter make it possible
the quantification in the presence of unknown interferents. This is
also reflected in the approaches followed for the estimation of figures
of merit.
While univariate calibration leads to relatively simple models, and
the associated uncertainty estimation and figures of merit are thoroughly
covered in several official documents, multivariate calibration does
not enjoy a similar status in this regard. Uncertainty estimation and
figures of merit for multivariate calibration methods have become subjects
of active research, especially in the field of chemometrics.
This work is intended as an introduction to multivariate calibration
from a chemometrics perspective and as a review of the various proposals
to generalizing the well-established univariate methodology to the multivariate
domain.
Uncertainty and figures of merit are subjects of interest to IUPAC's
Analytical Chemistry Division, as established within the general aims
of the Analytical Chemistry Division, and also in the Terms of Reference
of its Interdivisional Working Party on Harmonization of Quality Assurance.
Progress:
Project completed - IUPAC Technical Report published in Pure
Appl. Chem.
78(3), 633-661, 2006
Last Update: 14 March 2006
<project announcement published in
Chem.
Int.
May/Jun 2005>