Multivariate statistics, applications

A. J. Charlton, W. H. Farrington, P. Brereton 2002, (Application of 1H NMR and multivariate statistics for screening complex mixtures quality control and authenticity of instant coffee), J. Agric. Food Chem. 50, 3098-3103. 

Piovoso, M. J., and Kosanovich, K. A., Applications of multivariate statistical methods to process monitoring and controller design, Int. J. Control 59(3), 743-765 (1994). 

In the following section, the calculation of the VolSurf parameters from GRID interaction energies will be explained and the physico-chemical relevance of these novel descriptors demonstrated by correlation with measured absorption/ distribution/metabolism/elimination (ADME) properties. The applications will be shown by correlating 3D molecular structures with Caco-2 cell permeabilities, thermodynamic solubilities and metabolic stabilities. Special emphasis will be placed on interpretation of the models by multivariate statistics, because a rational design to improve molecular properties is critically dependent on an understanding of how molecular features influence physico-chemical and ADME properties. 

Bakraji, E. H., Othman, I., Sarhil, A., and Al-Somel, N. (2002). Application of instrumental neutron activation analysis and multivariate statistical methods to archaeological Syrian ceramics. Journal of Trace and Microprobe Techniques 20 57-68. 

This book is the result of a cooperation between a chemometrician and a statistician. Usually, both sides have quite a different approach to describing statistical methods and applications—the former having a more practical approach and the latter being more formally oriented. The compromise as reflected in this book is hopefully useful for chemometricians, but it may also be useful for scientists and practitioners working in other disciplines—even for statisticians. The principles of multivariate statistical methods are valid, independent of the subject where the data come from. Of course, the focus here is on methods typically used in chemometrics, including techniques that can deal with a large number of variables. Since this book is an introduction, it was necessary to make a selection of the methods and applications that are used nowadays in chemometrics. 

Peter Filzmoser was bom in 1968 in Weis, Austria. He studied applied mathematics at the Vienna University of Technology, Austria, where he wrote his doctoral thesis and habilitation, devoted to the field of multivariate statistics. His research led him to the area of robust statistics, resulting in many international collaborations and various scientific papers in this area. His interest in applications of robust methods resulted in the development of R software packages. J ( He was and is involved in the organization of several y scientific events devoted to robust statistics. Since... 

Despite the broad definition of chemometrics, the most important part of it is the application of multivariate data analysis to chemistry-relevant data. Chemistry deals with compounds, their properties, and their transformations into other compounds. Major tasks of chemists are the analysis of complex mixtures, the synthesis of compounds with desired properties, and the construction and operation of chemical technological plants. However, chemical/physical systems of practical interest are often very complicated and cannot be described sufficiently by theory. Actually, a typical chemometrics approach is not based on first principles—that means scientific laws and mles of nature—but is data driven. Multivariate statistical data analysis is a powerful tool for analyzing and structuring data sets that have been obtained from such systems, and for making empirical mathematical models that are for instance capable to predict the values of important properties not directly measurable (Figure 1.1). 

The focus is on multivariate statistical methods typically needed in chemo-metrics. In addition to classical statistical methods, also robust alternatives are introduced which are important for dealing with noisy data or with data including outliers. Practical examples are used to demonstrate how the methods can be applied and results can be interpreted however, in general the methodical part is separated from application examples. 

Application of multivariate statistics to fatty acid data from the Tyrolean Iceman and other mummies is a mosaic stone in the investigation of this mid-European ancestor, which is still a matter of research (Marota and Rollo 2002 Murphy et al. 2003 Nerlich et al. 2003). The iceman is on public display in the South Tyrol Museum of Archaeology in Bolzano, Italy, stored at —6°C and 98% humidity, the conditions as they probably were during the last thousands of years. 

A principal components multivariate statistical approach (SIMCA) was evaluated and applied to interpretation of isomer specific analysis of polychlorinated biphenyls (PCBs) using both a microcomputer and a main frame computer. Capillary column gas chromatography was employed for separation and detection of 69 individual PCB isomers. Computer programs were written in AMSII MUMPS to provide a laboratory data base for data manipulation. This data base greatly assisted the analysts in calculating isomer concentrations and data management. Applications of SIMCA for quality control, classification, and estimation of the composition of multi-Aroclor mixtures are described for characterization and study of complex environmental residues. 

The use of multivariate statistics to decipher multivariate data dates back to the 1930s (Hotelling) [3], and most early applications of these tools were in the fields of psychology, sociology and economics - fields where large amounts of highly unspecific data are the rule, rather than the exception. 

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. ... 

Chemometrics, as defined by Kowalski (1), includes the application of multivariate statistical methods to the study of chemical problems. SIMCA (Soft Independent Method of Class Analogy) and other multivariate statistical methods have been used as tools in chemometric investigations. SIMCA, based on principal components, is a multivariate chemometric method that has been applied to a variety of chemical problems of varying complexity. The SIMCA-3B program is suitable for use with 8- and 16-bit microcomputers. 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis. Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented. 

In the present time with almost unlimited computer facilities in the analytical laboratory, analytical chemists should be able to obtain substantial benefits from the application of time series, information theory, multivariate statistics, a.o. factor analysis and pattern recognition, operations research, numerical analysis, linear algebra, computer science, artificial intelligence, etc. This is in fact what chemo-metricians have been doing for the past decades. 

Many applications of GC-MS and HPLC-UV-VIS prove the powerful capabilities of these methods to analyze complex mixtures. The principal limiting factor is the obtainable separation, which can be optimized as described in section 3.1. When the physico-chemical separation is incomplete, a mathematical improvement of the resolution can be considered by the application of multivariate statistics. 

Innovative multivariate statistical analyses, such as artificial neural network (ANN) and genetic algorithms (GAs), were also used in order build regression models with real predictive capability and applicable to unknown samples. 

The molecular specificity of Fourier transform infrared (FTIR) lends itself quite well to applications in pharmaceutical development labs, as pointed out in a review article with some historical perspective.10 One of the more common applications of mid-IR in development is a real-time assessment of reaction completion when used in conjunction with standard multivariate statistical tools, such as partial least squares (PLS) and principal component analysis (PCA).18,19 Another clever use of FTIR is illustrated in Figure 9.1, where the real-time response of a probe-based spectroscopic analyzer afforded critical control in the charge of an activating agent (trifluoroacetic anhydride) to activate lactol. Due to stability and reactivity concerns, the in situ spectroscopic approach was... 

The concept of the PCSA method is general and this method should be applicable to many types of multivariate calibration techniques. As near-infrared and other spectroscopic methods are developed further for noninvasive in vivo clinical measurements, it is critical to understand the chemical basis of measurement selectivity. Unfortunately, calibration models generated from multivariate statistics are typically accepted without further investigation. Application of the PCSA method can help to establish the chemical or spectroscopic basis of predicted concentrations. 

Because data analysis is of central interest, particularly in the application of chemometric methods in the field of environmental research, a rough list of important multivariate statistical methods is given below (Tab. 1-1). 

Fax, L. Angewandte Statistik, Springer, Berlin, Heidelberg, New York, 1978 Flury, B., Riedwyl, H. Multivariate Statistics A Practical Approach, Chapman and Hall, 1988 Goldstein, M., Dillon, W.R. Multivariate Analysis Methods and Applications, Wiley, New York, 1984 Graham, R.C. Data Analysis for the Chemical Sciences A Guide to Statistical Techniques, VCH, New York, Weinheim, Cambridge, 1993... 

Identification of the pollutant pattern Application of multivariate statistical methods (see, for example, Section 9.2) for the detection of emitters or origins. 

The main aim of this part of the book is to demonstrate the advantages of using multivariate statistical computations. The application of chemometric methods to the results of routine environmental monitoring and their relevant interpretation facilitates asserta-tions concerning the identification of effective factors in the environment and the objective assessment of pollutant loading. These factors and loading states are either not accessible or are of only very restricted accessibility in current environmental monitoring. 

To demonstrate the accuracy, two dust and two soil reference materials were analyzed with the described method. The mean value of the correlation coefficients between the certified and the analyzed amounts of the 16 elements in the samples is r = 0.94. By application of factor analysis (see Section 5.4) the square root of the mean value of the communahties of these elements was computed to be approximately 0.84. As frequently happens in the analytical chemistry of dusts several types of distribution occur [KOM-MISSION FUR UMWELTSCHUTZ, 1985] these can change considerably in proportion to the observed sample size. In the example described the major components are distributed normally and most of the trace components are distributed log-normally. The relative ruggedness of multivariate statistical methods against deviations from the normal distribution is known [WEBER, 1986 AHRENS and LAUTER, 1981] and will be tested using this example by application of factor analysis. 

By application of multivariate statistical methods for consideration of the overall environmental situation of a river it is possible to optimize the sampling strategy. 

Sediment analyses are useful for characterization of pollution over a long period [MULLER, 1981]. Assessment of the state of a river and of the interactions between the components can be made by application of multivariate statistical methods only, because the strongly scattering territorial and temporal courses [FORSTNER and MULLER, 1974 FORSTNER and WITTMANN, 1983] are not compatible with many univariate techniques. FA shall serve as a tool for the recognition of variable structures and for the differentiated evaluation of the pollution of both river water and sediment [GEISS and EINAX, 1991 1992],... 

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