Bayesian Field Theory

Jörg C. Lemm

• Publisher: Johns Hopkins University Press
• Year: 2003
• eBook ISBN: 9780801877971
• Topic: Physical Sciences
• Subtopic: Applied Mathematics

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.

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Contents
• List of Figures
• List of Tables
• List of Numerical Case Studies
• Acknowledgments
• 1 Introduction
• 2 Bayesian framework
• 3 Gaussian prior factors
• 4 Parameterizing likelihoods: Variational methods
• 5 Parameterizing priors: Hyperparameters
• 6 Mixtures of Gaussian prior factors
• 7 Bayesian inverse quantum theory (BIQT)
• 8 Summary
• A: A priori information and a posteriori control
• B: Probability, free energy, energy, information, entropy, and temperature
• C: Iteration procedures: Learning
• Bibliography
• Index
• Footnotes