Statistical spectroscopy, applications

H. Mark and J. Workman, Jr., Statistics in Spectroscopy, 2nd ed. (Amsterdam Elsevier, 2003) J. E. DeMuth, Basic Statistics and Pharmaceutical Statistical Applications (New York Marcel Dekker, 1999) and R. N. Forthofer and E. S. Lee, Introduction to Biostatistics (San Diego Academic Press, 1995). 

Leurgans SE, Ross RT, Multilinear models applications in spectroscopy, Statistical Science, 1992,7, 289-319. 

Improvements in the computer technology associated with spectroscopy have also led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics. There is a large amount of information now available regarding chemometrics, but a detailed discussion is beyond the scope of this present book. However, we will look briefly at several multivariate-data analytical methods that are used for the analysis of FT-IR data, without detailing the mathematics associated with such methods. The most commonly used methods in infrared spectroscopy are as follows ... 

Tools from Mathematical Statistics Statistical Description of Random Variables and Stochastic Processes. Point Processes. - Theory The Optical Field A Stochastic Vector Field or. Classical Theoiy of Optical Coherence. Photoelectron Events A Doubly Stochastic Poisson Process or Theory of Photoelectron Statistics. - Applications Applications to Optical Communication. Applications to Spectroscopy. 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

Spectroscopic Methods, [Biological] Applications of Spectroscopy, EPR, Recent Advances in (Smaller). Spectroscopy, Infrared, Use in Biology (Lecomte). Spectroscopy of Transition-Group Complexes (Jorgensen) Statistical-Mechanical Theory of Transport Processes. X. The Heat of Transport in Binary Liquid Systems (Bearman, Kirkwood, Fixman). ... 

Under the same optical configuration, FCS (Fluorescence Correlation Spectroscopy) measurements (see Section 11.3) can be carried out on samples at the singlemolecule level under conditions where the average number of fluorescent molecules in the excitation volume is less than 1. It should be noted that at low fluorophore concentrations, the time required to obtain satisfactory statistics for the fluctuations may become problematic in practical applications (e.g. for a concentration of 1 fM, a fluorophore crosses a confocal excitation volume every 15 min). 

Recently, introductory books about chemometrics have been published by R. G. Brereton, Chemometrics—Data Analysis for the Laboratory and Chemical Plant (Brereton 2006) and Applied Chemometrics for Scientists (Brereton 2007), and by M. Otto, Chemometrics—Statistics and Computer Application in Analytical Chemistry (Otto 2007). Dedicated to quantitative chemical analysis, especially using infrared spectroscopy data, are A User-Friendly Guide to Multivariate Calibration and Classification (Naes et al. 2004), Chemometric Techniques for Quantitative Analysis (Kramer 1998), Chemometrics A Practical Guide (Beebe et al. 1998), and Statistics and Chemometrics for Analytical Chemistry (Miller and Miller 2000). 

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

DRIFT-IR) spectroscopy was also used for polymorphic characterization. The authors detail the application of multivariate techniques, multivariate statistical process control (MSPC), PC A and PLS, to the spectroscopic data for a simple yet powerful, rapid evaluation of the given crystalhzation process. ... 

Roggo, Y., Duponchel, L., and Huvenne, J.-P. (2003), Comparison of supervised pattern recognition methods with McNemar s statistical test Application to qualitative analysis of sugar beet by near-infrared spectroscopy, Anal. Chim. Acta, All, 187-200. 

In other cases, a baseline corrected peak height for a particular absorber may be employed as a term in the equation. In such a case, the wavelength difference on either side of a peak maximum will affect the contribution of that complex term. That increment or gap, in fact, under such circumstances becomes a part of the calibration. It is as important a contribution to the calibration as the coefficients on the wavelength terms. In this correlation spectroscopy, classical band assignments are not always possible. Little specific near-infrared literature exists in advance of most applications and it is not always possible to predict which wavelengths will produce the best linearity and the best sensitivity for a given analytical problem. In the empirical approach a variety of statistical treatments have been attempted. By far the most... 

Infrared spectroscopy has been shown to spectrally discriminate normal and malignant tissues in conjunction with statistical analysis methods, many of these mathematical methods are applicable to Raman spectral analysis. 

In the following sections, we review the application of Raman spectroscopy to glucose sensing in vitro. In vitro studies have been performed using human aqueous humor (HAH), filtered and unfiltered human blood serum, and human whole blood, with promising results. Results in measurement accuracy are reported in root mean squared error values, with RMSECV for cross-validated and RMSEP for predicted values. The reader is referred to Chapter 12 for discussion on these statistics. 

Adams, M.J. Chemometrics in Analytical Spectroscopy, Royal Society of Chemistry, Cambridge, 1995 Adler, B. Computerchemie - eine Einfuhrung, Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1986 Aitchison, J. The Statistical Analysis of Compositional Data, Chapman and Hall, London, 1986 Armanino, C. (Ed.) Chemometrics and Species Identification, Topics in Current Chemistry, Vol. 141, Springer, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987 Brereton, R.G. Chemometrics. Applications of Mathematics and Statistics to Laboratory Systems, Ellis Horwood, Chichester, 1990... 

One of the benefits that quantum theory has for chemistry is an improved understanding of elemental periodicity, spectroscopy and statistical thermodynamics topics which can be developed without reference to the nature of electrons, atoms or molecules. The success of these applications depend on approximations to model many-electron atoms on the hydrogen solution and the recognition of spin as a further component of electronic angular momentum, subject to the secondary condition known as (Pauli s) exclusion principle. 

Depending on the circumstances at hand, several different types of mean comparisons can be made. In this section we review the method for comparison of two means with independent samples. Other applications, such as a comparison of means with matched samples, can be found in statistical texts. Suppose, for example, we have two methods for the determination of lead (Pb) in orchard leaves. The first method is based on the electrochemical method of potentiometric stripping analysis [1], and the second is based on the method of atomic absorption spectroscopy [2], We perform replicate analyses of homogeneous aliquots prepared by dissolving the orchard leaves into one homogeneous solution and obtain the data listed in Table 3.1. 

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