Statistical overlap models

The results of Tables I, II and III confirm the general applicability of the peak overlap model, developed from point statistics, to randomly generated chromatograms. Individual exceptions to the model will undoubtedly be found as experimental testing Is conducted, but, overall, we anticipate modestly good predictions of m from high resolution chromatographic separations when the components are distributed randomly-... 

As all live plant and animal studies incorporate the distributive process, they are currently assailable only through statistical analysis of experimental data. These restrictions focus the area of modeling and statistical overlap clearly at the vitro stage of reversible and irreversible inhibition, areas where all techniques enter the arena. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Davis, J.M. (1997a). Justification of probability density function for resolution in statistical models of overlap. Chromatographia 44, 81. 

Rowe, K., Davis, J.M. (1995). Relaxation of randomness in two-dimensional statistical model of overlap theory and verification. Anal. Chem. 67, 2981. 

The statistical model of peak overlap clearly explains that the number of observed peaks is much smaller than the number of components present in the sample. The Fourier analysis of multicomponent chromatograms can not only identify the ordered or disordered retention pattern but also estimate the average spot size, the number of detectable components present in the sample, the spot capacity, and the saturation factor (Felinger et al., 1990). Fourier analysis has been applied to estimate the number of detectable components in several complex mixtures. 

The statistical prediction error is in concentration units and represents the uncertainty in the predicted concentrations due to deviations from the model assumptions, measurement noise, and degree of overlap of the pure spectra. As the system deviates from the underlying assumptions of CLS, the residual... 

Similarly, AHu°(W — W + E) is of opposite sign to the expected structural hydration contribution of E (28). There does not seem to be too much specificity in the interactions involving U which probably acts as a statistical structure breaker the local U-W interactions are probably not too different from the W-W ones, but the long-range ordering is destroyed. Schrier et al. (28) have interpreted the Bue parameters in terms of a destructure overlap cosphere model. Since... 

It is noteworthy that comparisons of existing assessment schemes reveal dissimilarities in the use of extrapolation methods and their input data between different jurisdictions and between prospective and retrospective assessment schemes. This is clearly apparent from, for example, a set of scientific comparisons of 5% hazardous concentration (HC5) values for different substances. Absolute HC5 values and their lower confidence values were different among the different statistical models that can be used to describe a species sensitivity distribution (SSD Wheeler et al. 2002a). As different countries have made different choices in the prescribed modeling by SSDs (regarding data quality, preferred model, etc.), it is clear that different jurisdictions may have different environmental quality criteria for the same substance. Considering the science, the absolute values could be the same in view of the fact that the assessment problem, the available extrapolation methods, and the possible set of input data are (scientifically) similar across jurisdictions. When it is possible, however, to look at the confidence intervals, the numerical differences resulting from different details in method choice become smaller because confidence intervals show overlap. 

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