General data analysis

There are two ways in which data can be analyzed using the MARS system. The first is through use of the general data analysis tools which are part of the standard MARS shell. The second is by means of specialized data analysis programming which can be invoked by the MARS shell. 

General Data Analysis and Parameter Estimation Tools ... 

A full account of the experimental method and general data analysis has been reported elsewhere (1-4). A brief summary of the features relevant to the present work is useful. 

This chapter gives a general introduction into the data analysis methodology. 

The data analysis module of ELECTRAS is twofold. One part was designed for general statistical data analysis of numerical data. The second part offers a module For analyzing chemical data. The difference between the two modules is that the module for mere statistics applies the stati.stical methods or rieural networks directly to the input data while the module for chemical data analysis also contains methods for the calculation ol descriptors for chemical structures (cl. Chapter 8) Descriptors, and thus structure codes, are calculated for the input structures and then the statistical methods and neural networks can be applied to the codes. 

Four general classes of HRA methods irc. (I) expert judgment, (2) performance process simulation, (3) performance data analysis, and (4) dependency calculations, ri.ese classes rue encompassed in the ten methods many of which contain multiple dassc.s of the methods. No attempt is made to dassity them according to the methods. 

As mentioned earlier some measures will be chosen because improvements in these areas were part of the project justification. It is most likely that these will be efficiency measures. Calculation of these measures generally requires analysis of data or specific data collection exercises. There is a relatively high cost associated with preparing these measures so they should be used prudently. In choosing efficiency measures, you should use only those where you have comparative data about the current management systems. For example, if there is no information on the number of hours dedicated to PSM and ESH, don t use this to try to demonstrate the improvement in efficiency. 

Figure 21.3 Modeling and simulation in the general context of the study of xenobiot-ics. The network of signals and regulatory pathways, sources of variability, and multistep regulation that are involved in this problem is shown together with its main components. It is important to realize how between-subject and between-event variation must be addressed in a model of the system that is not purely structural, but also statistical. The power of model-based data analysis is to elucidate the (main) subsystems and their putative role in overall regulation, at a variety of life stages, species, and functional (cell to organismal) levels. Images have been selected for illustrative purposes only. See color plate.

In a general way, we can state that the projection of a pattern of points on an axis produces a point which is imaged in the dual space. The matrix-to-vector product can thus be seen as a device for passing from one space to another. This property of swapping between spaces provides a geometrical interpretation of many procedures in data analysis such as multiple linear regression and principal components analysis, among many others [12] (see Chapters 10 and 17). 

Eigenvector projections are those in which the projection vectors u and v are eigenvectors (or singular vectors) of the data matrix. They play an important role in multivariate data analysis, especially in the search for meaningful structures in patterns in low-dimensional space, as will be explained further in Chapters 31 and 32 on the analysis of measurement tables and general contingency tables. 

Procrustes analysis has been generalized in two ways. One extension is that more than two data sets may be considered. In that case the algorithm is iterative. One then must rotate, in turn, each data set to the average of the other data sets. The cycle must be repeated until the fit no longer improves. Procrustes analysis of many data sets has been applied mostly in the field of sensory data analysis [4]. Another extension is the application of individual scaling to the various data sets in order to improve the match. Mathematically, it amounts to multiplying all entries in a data set by the same scalar. Geometrically, it amounts to an expansion (or... 

The determination and analysis of sensory properties plays an important role in the development of new consumer products. Particularly in the food industry sensory analysis has become an indispensable tool in research, development, marketing and quality control. The discipline of sensory analysis covers a wide spectrum of subjects physiology of sensory perception, psychology of human behaviour, flavour chemistry, physics of emulsion break-up and flavour release, testing methodology, consumer research, statistical data analysis. Not all of these aspects are of direct interest for the chemometrician. In this chapter we will cover a few topics in the analysis of sensory data. General introductory books are e.g. Refs. [1-3]. 

A powerful technique which allows to answer such questions is Generalized Procrustes Analysis (GPA). This is a generalization of the Procrustes rotation method to the case of more than two data sets. As explained in Chapter 36 Procrustes analysis applies three basic operations to each data set with the objective to optimize their similarity, i.e. to reduce their distance. Each data set can be seen as defining a configuration of its rows (objects, food samples, products) in a space defined by the columns (sensory attributes) of that data set. In geometrical terms the (squared) distance between two data sets equals the sum over the squared distances between the two positions (one for data set and one for Xg) for each object. 

This measurement methodology and data analysis is general and can be extended to other porous media. The results from MRI moisture profiles can also be used to measure moisture diffusivity that enable moisture transport models to be developed for a wide range of materials. 

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