## 2 Accuracy of Predictive Methods and What Is Required
### Why do Methods often not Perform up to the Required Level of Accuracy and Reliability?
When looking at the molecular descriptors based and the Group Contribution methods these are, when appropriately developed, methods that can be applied 'on the fly' and, except for constructing the methods, can be used by practitioners without having detailed knowledge of the methodologies behind. Ad _(ii) No optimal parametrization of statistical methods and GC methods_ relates to the way one performs the fitting of the adjustable parameters in both methods. Once a set of properly screened (see previous paragraph) experimental data has been obtained, the fitting of the adjustable parameters can start. Although there is no need from a mathematical point of view, many of the statistical methods that are being applied involve linear models. There is, however, no physical reason why linear models would be sufficient to describe and properly predict physicochemical properties of chemicals of various kind. Many might argue and not without reason, that practice has shown that such methods work and indeed they do. A problem arises when we want to go for the, what we have called, required accuracy and reliability. Moreover, often a pre-filtering is applied which reduces the number of molecular descriptors taken into account, most of the time accomplished by a Principal Component Analysis. On the one hand, this procedure prevents overfitting (many parameters to be fitted without having an overwhelmingly larger number of experimental input data for the fitting) but on the other hand one retains typically 90-95% of the variability which implies that the required accuracy (see also the discussion in the Introduction) which often requires R\({}^{2}\) =99% or even more, see Section 2, will not be achieved. Another reason that might lead to sub-optimal results relates to the way how the entire fitting is accomplished. When the total number of available experimental data is taken at once and the selected method parametrized using this data set, it is by no means guaranteed that this leads to a unique and best possible solution. This is what the authors explicitly saw when developing the GC method that finally led to the long-desired 1'kcal/mole accuracy' with no larger outliers [32]. It was found particularly helpful to look for trends among the molecules with larger outliers or incidental outliers which turned out strange as similar molecules were described very well. For instance, after one of the models was constructed and the root-mean-square deviation already better than that of at the time existing models, it was observed that molecules with a -NO\({}_{2}\) group has a severe error in the heat of formation and those with two NO\({}_{2}\) groups about twice that error. It turned out necessary to fit NO\({}_{2}\) containing molecular data first and then more or less fix (some flexibility should be left) the group parameters related to the NO\({}_{2}\) group and subsequently optimizing all other parameters. Also, third order groups, accounting for distant effects such as conjugation, turned out to be crucial. This is an iterative process, but, in the end, we obtained a result that was very satisfactory and a standard deviation of less than 3 kJ/mole and a maximum deviation of 10 kJ/mole for a widely varying set of organic molecules. When dealing with a different property, the type of third order groups might need to be chosen differently, so in fact different physical properties require a slightly different selection of terms which are, though not in a direct way, related to the different physical nature of the different properties. Ad (iii) Quality of dataThis requires serious attention when we use methods that require data fitting such as QSPR and Group Contribution methods. The source of data must reliable but even in good data sets errors of different kind occur. Depending on the magnitude of the error and the characteristics of the molecule concerned, for example does it involve special combination of chemical group, not removing erroneous data can either have a small or a detrimental effect on the quality of the methods.