Discriminant analysis density-based methods

If one does not wish to bias the boundaries of the NO region of a system, kernel density estimation (KDE) can be used to find the contours underneath the joint probability density of the PC pair, starting from the one that captures most of the information. Below, a brief review of KDE is presented first that will be used as part of the robust monitoring technique discussed in Section 7.7. Then, the use of kernel-based methods for formulating nonlinear Fisher s discriminant analysis (FDA) is discussed. 

This mechanistic question is one of the examples of the success of density functional theory methods in organometallic chemistry. Earlier work on the reaction mechanism could not discriminate between the two alternatives. Analysis of the different orbitals based on extended Hiickel calculations came to the result that the [3+2] pathway is more likely, but could not exclude the possibility of a [2+2] pathway [13]. Similar conclusions where obtained from the results of Hartree-Fock calculations in combination with QCISD(T) single point calculations [21], Attempts to use Ru04 as a model for osmium tetraoxide indicated that the formation of an oxetane is less favorable compared to the [3+2] pathway, but still possible [22, 23],... 

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