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Bayesian Field Theory

, 432 pages
May 2003
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Bayesian Field Theory

Ask a traditional mathematician the likely outcome of a coin-toss, and he will reply that no evidence exists on which to base such a prediction. Ask a Bayesian, and he will examine the coin, conclude that it was probably not tampered with, and predict five hundred heads in a thousand tosses; a subsequent experiment would then be used to refine this prediction. The Bayesian approach, in other words, permits the use of prior knowledge when testing a hypothesis.

Long the province of mathematicians and statisticians, Bayesian methods are applied in this ground-breaking book to problems in cutting-edge physics. Joerg Lemm offers practical examples of Bayesian analysis for the physicist working in such areas as neural networks, artificial intelligence, and inverse problems in quantum theory. The book also includes nonparametric density estimation problems, including, as special cases, nonparametric regression and pattern recognition. Thought-provoking and sure to be controversial, Bayesian Field Theory will be of interest to physicists as well as to other specialists in the rapidly growing number of fields that make use of Bayesian methods.

Jörg C. Lemm is a former teacher of physics and psychology at the University of Muenster, Germany, and has worked in the areas of statistics, decision theory, and neural networks.

"There is a considerable amount of interesting discussion on inference generally and, in particular, on Bayesian inference. While a statistician might find the language and point-of-view somewhat different, this is a useful resource for those curious about the use of statistics in modern physics."

"Thought-provoking and challenging."

"The value of a statistical method outlined by [the Rev. Thomas] Bayes in 1763 has become increasingly apparent and has resulted in a blossoming of 'Bayesian' methods in scientific fields ranging from archeology to computing."

"Very well written and well organized. The approach is original and deserves to be widely known. This is an excellent book."

"Lemm's approach is original and very fruitful, and deserves to be widely known. Even for the insider the book is a source of new ideas and applications. The last chapter on inverse quantum theory is expected to be of great importance in the growing fields of quantum information processing and atomic force spectroscopy."

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