Statistical parameters model

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC. 

A variety of statistical parameters have been reported in the QSAR literature to reflect the quality of the model. These measures give indications about how well the model fits existing data, i.e., they measure the explained variance of the target parameter y in the biological data. Some of the most common measures of regression are root mean squares error (rmse), standard error of estimates (s), and coefficient of determination (R2). 

A more detailed analysis using multivariable regression of the ibuprofen data demonstrated that a three-parameter model accurately fit the data (Table 7). The Bonding Index and the Heywood shape factor, a, alone explained 86% of the variation, while the best three-variable model, described in what follows, explained 97% of the variation and included the Bonding Index, the Heywood shape factor, and the powder bed density. All three parameters were statistically significant, as seen in Table 7. Furthermore, the coefficients are qualitatively as... 

The best statistical parameters were obtained by correlating the in vivo selectivity with the Vdif descriptor defined with respect to the oqa-AR supermolecule. It is worth noting that the oqa is the adrenergic receptor subtype of functional relevance for the urethra tissue (dog model) [8]. Thus, ligands showing high potency and selectivity for the lower urinary tract are those, which better fit the volume of the supermolecule that represents the binding site of the ala-AR subtype. 

The reliability of initial equations and regulations was proved with numerous calculations and comparisons. In particular, it was shown [8] that PE-parameter numerically equals the energy of valence electrons in a statistical atom model and is a direct characteristic of electron density in the atom at the given distance from the nucleus. 

Various models for BBB permeability prediction are summarized in terms of their data sets, methods employed, statistical parameters and descriptors, important outcomes in Tables 22.1 and 22.2, respectively. 

Table 22.1 Data sets, methods and statistical parameters of the models... 

In this equation, n denotes the number of observations (i.e., data points), r is the correlation coefficient, i is the standard deviation of the residuals, F is the value of the Fisher test for the significance of the equation, and the P-value denotes the statistical significance level. The values in parenthesis of this QSPR equation indicate the 95% confidence inferval of fhe estimated coefficients. From the statistical parameters it can be derived that this QSPR model is significant at the 99% confidence level. 

Current methods for supervised pattern recognition are numerous. Typical linear methods are linear discriminant analysis (LDA) based on distance calculation, soft independent modeling of class analogy (SIMCA), which emphasizes similarities within a class, and PLS discriminant analysis (PLS-DA), which performs regression between spectra and class memberships. More advanced methods are based on nonlinear techniques, such as neural networks. Parametric versus nonparametric computations is a further distinction. In parametric techniques such as LDA, statistical parameters of normal sample distribution are used in the decision rules. Such restrictions do not influence nonparametric methods such as SIMCA, which perform more efficiently on NIR data collections. 

In the literature, QPPRs are represented with varying details about the model derivation process. Statistical parameters, training and evaluation set information, and specification of the applicability range differ from publication to publication. Although guidelines for the application of QPPRs and QSPRs have been proposed [26], they are not always followed consistently. In this book, QPPRs are presented in the following form ... 

Coefficients ao and a and the statistical parameters derived for three classes for compounds are presented in Table 13.3.1. Model 13.3.1 allows order of magnitude estimations for Kow but does not account for particular substitution patterns. 

Nearly all theories to date predict that IETS intensities should be proportional to n, the surface density of molecular scatterers. Langan and Hansma (21) used radioactively labeled chemicals to measure a surface concentration vs solution concentration curve ( Fig. 10 ) for benzoic acid on alumina using the liquid doping technique. The dashed line in Fig. 10 is a 2 parameter fit to the data using a simple statistical mechanical model by Cederberg and Kirtley (35). This model matched the free energy of the molecule on the surface with that in solution. The two parameters in this model were the surface density of binding sites ( 10" A )... 

Using the so-called planar libration-regular precession (PL-RP) approximation, it is possible to reduce the double integral for the spectral function to a simple integral. The interval of integration is divided in the latter by two intervals, and in each one the integrands are substantially simplified. This simplification is shown to hold, if a qualitative absorption frequency dependence should be obtained. Useful simple formulas are derived for a few statistical parameters of the model expressed in terms of the cone angle (5 and of the lifetime x. A small (3 approximation is also considered, which presents a basis for the hybrid model. The latter is employed in Sections IV and VIII, as well as in other publications (VIG). 

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