Overlap, component, statistical model

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. 

With sufficiently complex samples, particularly biological and environmental samples, the frequency of overlap can be estimated by statistical means. In a statistical model developed by Davis and this author [33], far-reaching conclusions follow from a simple basic assumption the probability that any small interval dx along the separation path x is occupied by a component peak center is A dx, where A is a constant. This assumption defines a Poisson process and leads to well-known statistical conclusions. 

Test of the Statistical Model of Component Overlap by Computer-Generated Chromatograms, J. C. Giddings, J. M. Davis, and M. R. Schure, in S. Ahuja, Ed., Ultrahigh Resolution Chromatography, ACS Symposium Series No. 250, American Chemical Society, Washington, DC, 1984, pp. 9-26. 

Test of the Statistical Model of Component Overlap by Computer-Generated Chromatograms... 

An earlier statistical model of component overlap Is reviewed. It Is argued that a statistical treatment Is necessary to reasonably Interpret and optimize high resolution chromatograms having substantial overlap. 

A series of computer-simulated chromatograms has been generated to test the validity of a procedure derived from the statistical model for calculating the number of randomly distributed components when many of them are obscured by overlap. Plots of the logarithm of the peak count versus reciprocal peak capacity are used for this purposTI TRese plots are shown to provide reasonable estimates of the total number of components In the synthetic chromatograms. 

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. 

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-... 

MLR is a method used to estimate the size and statistical significance of the relationship between a dependent variable (y) and one independent or predictor variable, (x ), after adjustment for confounders (X2,...). As discussed earlier, models constructed from spectroscopy are relatively simple due to linear combinations of the instrumental measurements. Models for a broader range of conditions (i.e., measurements from several wavelengths) have been constructed in order to separate overlapping peaks elicited from the analyte plus other unknown components or conditions. These multiple linear methods for separating outliers are based upon the following equation ... 

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