Class method univariate

Two main classes of method, univariate and multivariate, are commonly employed. Univariate methods... 

As introduced in the previous section, class and sectional methods are based on a discretization of the internal coordinate so that the GPBE becomes a set of macroscopic balances in state space. Indeed, the fineness of the discretization will be dictated by the accuracy needed in the approximation of the integrals and derivative terms appearing in the GPBE. As has already been anticipated, the methods differ according to the number of internal coordinates used in the description and depend on the nature of the internal coordinates. Therefore, in what follows, we will discuss separately the univariate, bivariate, and multivariate PBE, and the use of these methods for the solution of the KE. 

As with class and sectional methods for univariate PBE, the particle-velocity magnitude space is uniformly discretized over M intervals of size A < 2 < 3 < < m-i <... 

In order to identify these metabolites, Catchpole et al. decided to use GC-TOF-MS, analysing 2,182 tubers ( 180 replicates per genotype) for 252 metabolite peaks. Roughly a third of metabolites were fully identified, a third partly known (class of compoimd) and a third unknown. Univariate statistical analyses were carried out systematically for all 252 metabolites, in addition to multivariate analyses using the methods already described. Two metabolites found in GM samples were not present in any of the conventional controls. The large mnnber of... 

FIGURE 21 Example of application of the potential function method for the discrimination of two classes in the univariate case graphical representation of (A) the cumulative potential and of (B) the posterior probability of class belonging for the two categories as a function of the value of the independent variable x. 

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