A Simple Question The Meaning of Chemometrics Pondered

This leads us to the other hand, which, it should be obvious, is that we feel that Chemometrics should be considered a subfield of Statistics, for the reasons given above. Questions currently plaguing us, such as How many MLR/PCA/PLS factors should I use in my model , Can I transfer my calibration model (or more importantly and fundamentally How can I tell if I can transfer my calibration model ), may never be answered in a completely rigorous and satisfactory fashion, but certainly improvements in the current state of knowledge should be attainable, with attendant improvements in the answers to such questions. New questions may arise which only fundamental statistical/probabilistic considerations may answer one that has recently come to our attention is, What is the best way to create a qualitative (i.e., identification) model, if there may be errors in the classifications of the samples used for training the algorithm  

In order to appreciate how understanding new statistical concepts can help us, let us look at an example of where we can better apply known statistical concepts, to understand phenomena currently afflicting us. To this end, let us pose the seemingly innocuous question When doing quantitative calibration, why is it that we use the formulation of the problem that makes the constituent values the dependent (i.e., the Y) variable, and make the spectroscopic data the X (or independent) variable, called the Inverse Beer s Law formulation (sometimes called the P-matrix formulation) (For that matter, why is the formulation that we most commonly use called Inverse Beer s Law instead of the direct Beer s Law ) 

we are sure that everybody reading this chapter thinks they know the answer. Now, if you are among those readers, then you are wrong already, because there are multiple answers to this question, all of them correct, and each of them incomplete. 

Let us dispose of the most common answer first. This answer is the one given in most of the discussions about the relative merits of the two formulations, e.g. [2], and is essentially a practical one we use the Inverse Beer s Law formulation because by doing so, we need to only determine the concentration(s) of the analyte(s) of interest. In the Beer s law formulation, you must determine the concentrations of all components in a mixture, whether they are of interest or not. Of course, there is benefit to that also as Malinowski points out, you can determine the number of components in a mixture and their spectra, as well as their concentrations, by proper application of the techniques of factor analysis in such a case [3], 

None of these answers deal with fundamentals. So finally we get to the substantive part of the discussion, the one that connects with our original diatribe concerning the goal 

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