Maximum-Entropy and Bayesian Methods in Science and Engineering: Foundations

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G. Erickson, C.R. Smith
Springer Science & Business Media, Aug 31, 1988 - Mathematics - 314 pages
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This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.
 

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Contents

How Does the Brain Do Plausible Reasoning?
1
THE RELATION OF BAYESIAN AND MAXIMUM ENTROPY METHODS
25
AN ENGINEER LOOKS AT BAYES
31
BAYESIAN INDUCTIVE INFERENCE AND MAXIMUM ENTROPY
53
Excerpts from Bayesian Spectrum Analysis and Parameter Estimation
75
DETECTION OF EXTRASOLAR SYSTEM PLANETS
147
STOCHASTIC COMPLEXITY AND THE MAXIMUM ENTROPY PRINCIPLE
161
THE AXIOMS OF MAXIMUM ENTROPY
173
Quantum Density Matrix and Entropic Uncertainty
235
INFORMATIONTHEORETICAL GENERALIZATION OF THE UNCERTAINTY PRINCIPLE
245
TIME ENERGY AND THE LIMITS OF MEASUREMENT
249
ON A DETECTION ESTIMATOR RELATED TO ENTROPY
257
THE EVOLUTION OF CARNOTS PRINCIPLE
267
A LOGIC OF INFORMATION SYSTEMS
283
METHODOLOGICAL PRINCIPLES OF UNCERTAINTY IN INDUCTIVE MODELLING
295
COMPARISON OF MINIMUM CROSSENTROPY INFERENCE WITH MINIMALLY INFORMATIVE INFORMATION SYSTEMS
305

UNDERSTANDING IGNORANCE
189
MAXIMUM ENTROPY CALCULATIONS ON A DISCRETE PROBABILITY SPACE
205

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