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Maximum-entropy models in science and engineering. (English) Zbl 0746.00014
New York: John Wiley & Sons. xii, 635 p. (1989).
This monograph is devoted to the maximum entropy principle (MEP) and covers a broad spectrum of applications. The MEP requires one to maximize the Bayesian (or Shannon) entropy (or some other appropriate measure of entropy) subject to all the given constraints being satisfied. The principle cannot be proven in a general setting, such as, e.g. the second law of thermodynamics. But it allows one to get the most homogeneous, appropriate probability distributions under the above-mentioned conditions.
The book is very nicely written. Many problematic points, e.g. the relationship between entropy and information, are explained clearly. The author, who is very active in the field, devotes more than half of the book to applications, e.g. to statistics, statistical thermodynamics, regional and urban planning, marketing and election, economics, finance, image reconstruction, spectral analysis, operation research and even to biology, medicine and ecology. The book can also be used as a textbook with many exercises. Bibliographical and historical remarks at the end of every chapter indicate rather extensive knowledge on the part of the author. The list of references is exhaustive.
It seems the method of MEP should be of help in solving new practical problems in the immediate future.

00A69 General applied mathematics
62B10 Statistical aspects of information-theoretic topics
82B35 Irreversible thermodynamics, including Onsager-Machlup theory
90B99 Operations research and management science
94A17 Measures of information, entropy