Qualitative model building

There are several circumstances where qualitative models can be very useful in PAT  

One needs to deploy an outlier- or fault-detection system, based on the analyzer outputs 

Poor precision of reference (y) data causes unacceptably large errors in quantitative models, and 

The inherent quantitative relationships between the x variables and the y variable are very nonlinear and very complex. 

Cases (2) and (3) reflect an inherent advantage of qualitative models over quantitative ones that it is not necessary to assume a quantitative relationship between the x variables and the y variable. This results in less burden on the regression modeling procedure, and more likelihood of generating an effective model. The disadvantages of qualitative models are that they generate less-specific results, and that they tend to be somewhat more complicated to implement in a real-time enviromnent. 

At first thought, one might be skeptical about the need for qualitative model building in the field of PAC, where the customer most often wants a meaningful number from the analyzer. However, there are several circumstances where qualitative models can be very useful in PAC  

Case 3 indicates a means by which a qualitative model can be used to support a quantitative model, and was discussed in Section 8.4.3. Case 4 is a special application for PAC, in which the on-line analyzer can be set up to serve as health monitor for the process. 

This section will focus on classification methods that are in the category of supervised learning, where a method is developed using a set of calibration data and complete prior knowledge about the classification of calibration samples. The other category, 

In order to better understand supervised learning methods, it is useful to recall the concept of spatial sample representation which was mentioned earlier in Section 8.2.7. The development of any supervised learning method involves three steps  

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Unfortunately, FfipFfop and HypoGen cannot process the large training sets of the size used for QSAR model building. The set of 29 most potent Cox2 inhibitors has been submitted to HipHop and the best of the resulting hypotheses has been qualitatively compared to the overlay-based QSAR model hypothesis. 

Kinetics Third The dynamic nature of chemistry becomes fully evident through kinetics. Our approach shows how insight and model building are critical to the indentification of reaction mechanisms. The full chapter on kinetics follows coverage of equilibrium however, qualitative kinetic arguments are used early to develop an understanding of equilibrium, and the full treatment can be used anywhere in the sequence. 

Successful model building is at the very heart of modern science. It has been most successful in physics but, with the advent of quantum mechanics, great inroads have been made in the modelling of various chemical properties and phenomena as well, even though it may be difficult, if not impossible, to provide a precise definition of certain qualitative chemical concepts, often very useful ones, such as electronegativity, aromaticity and the like. Nonetheless, all successful models are invariably based on the atomic hypothesis and quantum mechanics. The majority, be they of the ah initio or semiempirical type, is defined via an appropriate non-relativistic, Born-Oppenheimer electronic Hamiltonian on some finite-dimensional subspace of the pertinent Hilbert or Fock space. Consequently, they are most appropriately expressed in terms of the second quantization formalism, or even unitary group formalism (see, e.g. [33]). 

The chemical and isotopic compositions of various earth materials now make up the data used to build models to explains the formation of the Earth, its evolution the genesis of the different terrestrial units continents, mantle, core, ocean etc.. .. From a descriptive and qualitative early stage, geochemistry has become explanatory and quantitative. In this new context modeling is a key method. 

The following sections focus on the description of these model scenarios and the major findings of the model application regarding the build-up of a hydrogen supply infrastructure. While the scenarios ( REF ) and ( REN-CCS ) are quantitatively analysed in more detail, the other scenarios are more qualitatively described. 

The essence of the model is to build up any reaction profile through the qualitative mixing of appropriate electronic configurations. Thus, just as the properties of molecular orbitals (energy, geometry) may be readily appreciated by analysis of the atomic orbitals from which they are derived, the essence of a reaction profile may be more readily comprehended by understanding the building blocks from which it is constructed. 

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