Statistics discipline

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Chemometrics is the discipline which deals wdth the application of statistical and, in a more general sense, of mathematical methods to chemical data. Chemometric methods are used for the extraction of chemical information from chemical data. 

Multivariate statistics is the discipline to analyze data, to elucidate the intrinsic structure within the data, and to reduce the number of variables needed to describe the data. 

It extends the usage of statistical methods and combines it with machine learning methods and the application of expert systems. The visualization of the results of data mining is an important task as it facilitates an interpretation of the results. Figure 9-32 plots the different disciplines which contribute to data mining. 

Molecular modeling has evolved as a synthesis of techniques from a number of disciplines—organic chemistry, medicinal chemistry, physical chemistry, chemical physics, computer science, mathematics, and statistics. With the development of quantum mechanics (1,2) ia the early 1900s, the laws of physics necessary to relate molecular electronic stmcture to observable properties were defined. In a confluence of related developments, engineering and the national defense both played roles ia the development of computing machinery itself ia the United States (3). This evolution had a direct impact on computing ia chemistry, as the newly developed devices could be appHed to problems ia chemistry, permitting solutions to problems previously considered intractable. 

Evidence of the appHcation of computers and expert systems to instmmental data interpretation is found in the new discipline of chemometrics (qv) where the relationship between data and information sought is explored as a problem of mathematics and statistics (7—10). One of the most useful insights provided by chemometrics is the realization that a cluster of measurements of quantities only remotely related to the actual information sought can be used in combination to determine the information desired by inference. Thus, for example, a combination of viscosity, boiling point, and specific gravity data can be used to a characterize the chemical composition of a mixture of solvents (11). The complexity of such a procedure is accommodated by performing a multivariate data analysis. 

Throughout the 1970s, appHcations of pattern recognition were found in the chemical sciences. Other methods of multivariate mathematics and statistics were borrowed or invented, and a new discipline called chemometrics arose. In 1974, the Chemometrics Society was formed, and the first Chemometrics newsletter came out in 1976 (12). 

The field of statistics as a separate discipline began m the early to mid nineteenth century among German, British, French, and Belgian social reformers, refeired to as statists i.e., those that were concerned with numbers related to the state, including crime rates, income distributions, etc. [34] The appeal of frequency-based interpretation of probability would have been natural m the study of large human populations. 

Statistics in general is a discipline dealing with ideas on description of data, implications of data (relation to general pharmacological models), and questions such as what effects are real and what effects are different Biological systems are variable. Moreover, often they are living. What this means is that they are collections of biochemical reactions going on in synchrony. Such systems will have an intrinsic variation in their output due to the variances in the... 

Thermodynamic, statistical This discipline tries to compute macroscopic properties of materials from more basic structures of matter. These properties are not necessarily static properties as in conventional mechanics. The problems in statistical thermodynamics fall into two categories. First it involves the study of the structure of phenomenological frameworks and the interrelations among observable macroscopic quantities. The secondary category involves the calculations of the actual values of phenomenology parameters such as viscosity or phase transition temperatures from more microscopic parameters. With this technique, understanding general relations requires only a model specified by fairly broad and abstract conditions. Realistically detailed models are not needed to un-... 

This fusion of disciplines, though desirable and inevitable, complicates the writing of books in fields where it occurs. Spectrochemical analysis by means of x-rays is definitely such a field. For whom shall a book on this subject be written Our answer is clear. This book was written for the analytical chemist who wants to use these x-ray methods and to understand them. We have striven for correctness in physics, electronics, and statistics but we have tried first of all to help the analytical chemist in his work. 

But chemical engineering is more than a group of basic industries or a pile of economic statistics. As an intellectual discipline, it is deeply involved in both basic and applied research. Chemical engineers bring a unique set of tools and methods to the study and solution of some of society s most pressing problems. 

We shall use the term "Log Normal" for reasons which will clear later. It should be now apparent that we use terms borrowed from statistics and a statistical approach to describe a distribution of particles. The two disciplines are well suited to each other since statistics is easily capable Of handling large assemblages, and the soUd state process with which we deal are random growth processes which produce large numbers of pcirticles. 

The various attempts, in the different fields, can be viewed as an effort to combine methods and experience of two disciplines which have reached since longtime their maturity quantum mechanics for isolated systems and statistical mechanics. This effort of combination produces important results, and the progress in this area is indisputable. 

In the last few years, detection, characterization, and handling of pollution sites have grown into a new discipline with its specific technology, initially drawn from other disciplines such as statistics, then customized to meet the specificity of pollution control. 

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]. 

Since 1992 a variety of related but much more powerful data-handling strategies have been applied to the supervised analysis of PyMS data. Such methods fall within the framework of chemometrics the discipline concerned with the application of statistical and mathematical methods to chemical data.81-85 These methods seek to relate known spectral inputs to known targets, and the resulting model is then used to predict the target of an unknown input.86... 

One often finds that when high resolution separation schemes are utilized, other techniques and disciplines must participate in the scheme of understanding and effectively utilizing the separation with subsequent identification of the resulting zones. A rigorous and often multidimensional detection scheme such as mass spectrometry and/or fluorescence is found both for the life science and industrial polymer applications. Other disciplines including informatics and statistics are often... 

The table is not exhaustive, although it does include a majority of experimental designs that are used. One-at-a-time designs are the usual non-statistical type of experiments that are often carried out by scientists in all disciplines. Not included explicitly, however, are experimental designs that are generated from combinations of listed items. For example, a multi-factor experiment may have several levels of some of the factors but only two levels of other factors. 

Nevertheless, at its very fundamental core, there is a very deep and close connection between the two disciplines. How could it be otherwise Chemometric concepts and techniques are based on principles that were formulated by mathematicians hundreds of years ago, even before the label Statistics was applied to the subfield of Mathematics that deals with the behavior and effect of random numbers on data. Nevertheless, recognition of Statistics as a distinct subdiscipline of Mathematics also goes back a long way, certainly long before the term Chemometrics was coined to describe a subfield of that subfield. 

Before we discuss the relationship between these two disciplines, it is, perhaps, useful to consider what they are. We have already defined Statistics as ... the study of the properties of random numbers. .. [3],... 

Biochips produce huge data sets. Data collected from microarray experiments are random snapshots with errors, inherently noisy and incomplete. Extracting meaningful information from thousands of data points by means of bioinformatics and statistical analysis is sophisticated and calls for collaboration among researchers from different disciplines. An increasing number of image and data analysis tools, in part freely accessible ( ) to academic researchers and non-profit institutions, is available in the web. Some examples are found in Tables 3 and 4. 

The prime objective of this concise review is to provide an illustration of the interaction of these two disciplines using particular examples. In choosing the examples, we seek to demonstrate the potentialities of the conformation-dependent design of the sequences of monomeric units in heteropolymer macromolecules. Under such a design, their chemical structure is controlled not only by the kinetic parameters of a reaction system but also by the conformational statistics of polymer chains. 

Matters are complicated further when we try to expand inter(trans)disciplinary work beyond natural sciences, including social sciences such as sociology, history, philosophy etc. This inevitably springs the trap of statistical debates and the factuali-zation of the research work of all the included disciplines. This is of course a dead end and will never ever lead to solutions with a broad consensus, which will also become politically important. 

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