Exploratory Data Analysis Using Fisher Information
Buch in deiner Nähe kaufen
Beschreibung
The basic goal of a research scientist is to understand a given, unknown system. This innovative book develops a systematic approach for achieving this goal. All science is ultimately dependent upon observation which, in turn, requires a flow of information. Fisher information, in particular, is found to provide the key to understanding the system. It is developed as a new tool of exploratory data analysis, and is applied to a wide scope of systems problems. These range from molecules in a gas to biological organisms in their ecologies, to the socio-economic organization of people in their societies, to the physical constants in the universe and, ultimately, to proto-universes in the multiverse.
Examples of system input-output laws discovered by the approach include the famous quarter-power laws of biology and the Tobin q-theory of optimized economic investment. System likelihood laws that can be determined include the probability density functions defining in situ cancer growth and a wide class of systems (thermodynamic, economic, cryptographic) obeying Schrodinger-like equations. Novel uncertainty principles in the fields of biology and economics are also found to hold.
B. Roy Frieden and Robert A. Gatenby are professors at the University of Arizona. Frieden is in the College of Optics, and Gatenby is Chairman of the Radiology Dept. at the Arizona Health Sciences Center. Frieden has pioneered the use of information for developing image restoration approaches, and for understanding the physics of unknown systems, both nonliving and living. Gatenby has actively promoted the study of information as a determinant of healthy and malignant growth processes, and has developed integrated mathematical models and empirical techniques for this purpose.
"Sustainability" is often used in a qualitative sense. However, there is at present a great need to quantitatively measure (and monitor) its many qualitative aspects in real systems. Real systems are regarded as sustainable if they can maintain their current, desirable productivity and character without creating unfavorable condi tions elsewhere or in the future [1-4]. Sustainability therefore incorporates both concern for the future of the current system (temporal sustainability) and concern about the degree to which some areas and cultures of the planet are improved at the expense of other areas and cultures (spatial sustainability). That is, sustainability is to hold over both space and time. Sustainability encompasses many disciplines. For example, economic systems are not sustainable if they degrade their natural resource base and impoverish some sectors of the human population [5, 6]. Indices are needed that will measure sustainability through time, and over space, at several scales. These indices must also have the ability to aggregate the many disciplinary facets of sustainability, often incorporatedthrough a large number of environmental, social, and economic variables. Such a multidisciplinary dynamic system can be regarded as sustainable if it maintains a desirable steady state or regime', including fluctuations that are desirable (such as those that respond to natural disturbances [8]).
Only book in which EPI, a form of information theory, is discussed in terms of its applications rather its theoretical underpinnings Valuable new approach for those working in data mining, pattern recognition, and algorithms and statistics Includes a first chapter that introduces the required math and the various ways in which Fisher information is used in research
This book uses a mathematical approach to deriving the laws of science and technology that is based upon the concept of Fisher information.
The approach that follows from these ideas is called the principle of Extreme Physical Information (EPI). It is shown how to use EPI to determine the theoretical input – output laws of unknown systems. Depending upon the system, these laws can be deterministic or stochastic and applicable to data used in many complex computational systems. Not only does information characterize the amount and quality of their data, but – much more basically – it can be used to analytically determine how the data arises out of the system, by the EPI principle. The book can be profitably read by someone whose level of math is at the level of an undergraduate degree in science or engineering.
Autor*in
Roy Frieden
Themen in »Exploratory Data Analysis Using Fisher Information«
EPI Entropy Estimation of Probability Laws Estimation of System Laws Fisher Information Fluctuations in Financial Issues Information Pattern Recognition Physical Information Power Laws Sociocultural Organization data analysis information theory organization uncertainty
Stimmen zu »Exploratory Data Analysis Using Fisher Information«
From the reviews:
"Roy Frieden has been exploring the consequences of studying physical phenomena on the basis of Fisher information and extreme physical information … . therefore wish to emphasize that the truly original feature of this book … is precisely its broad coverage; its demonstration that such a simple principle, easily grasped, is capable of yielding valuable results in such a wide range of fields of enquiry. I found Frieden’s earlier books immensely original and intellectually thrilling and this one adds yet more weight to that opinion." (P. W. Hawkes, www.amazon.com, October, 2007)
"I personally have used and exploited the Fisher information theme in numerous papers related to quantum mechanics and relativity, in particular via relations of FI to the quantum potential. I would even say that this theme seems to have ‘cosmic significance’ and in the present arena of information technology, processing, retrieval, and distortion the book should be considered as must reading." (Robert Carroll, www.amazon.com, October, 2007)
"The book begins with an introduction by Frieden, which covers Fisher information and its uses when employing the EPI approach. … This fascinating book is well organized, written in a careful and systematic way, and contains much new material. It will be useful to those interested in information technology (IT), processing, retrieval, and distortion. It is an excellent source of information for the study and research of exploratory data analysis." (P. R. Parthasarathy, ACM Computing Reviews, Vol. 49 (8), August, 2008)
()