Exploratory Data Analysis Using Fisher Information
Description
Reviews / Votes
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)
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Persons
Professor Emeritus - B. Roy Frieden:
B.S., M.S., Ph.D., Professor of Optical Sciences, Univ. of Arizona 1966-2002; books "Probability, Statistical Optics and Data Testing" (Springer-Verlag, 3rd ed., 2001), "Physics from Fisher Information" (Cambridge Univ. Press, 1998), "Science from Fisher Information" (Cambridge Univ. Press, 2004); inventor of principle of Extreme physical information (EPI)
Dr. Robert A. Gatenby:
BSE, Princeton Univ. MD, University of Pennsylvania.
Content
AUDREYL. MAYER, CHRISTOPHER W. PAWLOWSKI, BRIAN D. FATH, ANDHERIBERTOCABEZAS
All organisms alter their surroundings, and humans now have the ability to affect environments at increasingly larger temporal and spatial scales. Indeed , mechanical and engineering advances of the twentieth century greatly enhanced the scale of human activities. Among these are the use and redistribution of natural resources . Unfortunately, these activities can have unexpected and unintended consequences. Environmental systems often respond to these activities with diminished or lost capacity of natural function. Fortunately, environmental management can play an important role in ameliorating these negative effects.
The aim is to promote sustainable development, i.e., enrichment of the lives of the majority of people without seriously degrading the diversity and richness of the environment. However, the management tools themselves often fall prey to the same narrow levels of perspective that generated the negative conditions. The challenge is to develop a system-level index, one that indicates the organizati on and direction of ecological system dynamics. This index could detect when the system is changing its configuration to a new, perhaps less desirable, dynamic regime and may be incorporated into a sustainable management plan for the system. In this chapter, we demonstrate the use of Fisher information (FI) as such an environmental system index.
7.1. Summary
We derive an expression for FI based on sampling of the system trajectory as it evolves in the phase space defined by the state variables of the system. This FI index is derived as a measure ofsystem dynami c order; as defined by its speed and acceleration along periodic steady-state trajectories. We illustrate the concepts on data collected from both computer model simulations and real-world environmental systems. PI is found to provide a valuable tool to identify impending and in-progress shifts in regime, as distinguished from normal cycles, fluctuations , and noise in the systems.
7.2. Introduction
"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 conditions 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."
