Bayesian Field Theory

Front Cover
JHU Press, 2003 M06 6 - 432 pages

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.

-- Achim Weiguny, Institut fuer Theoretische Physik

From inside the book

 

Selected pages

Contents

Gaussian prior factors
3
Variational methods
4
Tables
8
Variational methods
167
Copyright

Other editions - View all

Bayesian Field Theory
Jörg C. Lemm
Limited preview - 2003
Bayesian Field Theory
Jörg C. Lemm
Limited preview - 2003

Common terms and phrases

algorithm analogous approximately periodic average Bayesian approach BIQS calculated components constraint corresponding data points data terms defined denotes density estimation dependent empirical density entropy equivalent kernel error functional Frequentist Gaussian likelihood Gaussian prior factor Gaussian processes Gaussian regression Hartree-Fock hyperfields hyperparameters implemented integral inverse covariance inverse quantum iteration Lagrange multiplier Laplacian smoothness likelihood model likelihood p(yx linear loss function matrix Maximum A Posteriori measurement minimization mixture models mutual information noise non-negativity nonparametric normalization null space obtained operator optimal overfitting parameterized parameters partition sums Pemp posterior predictive density prior covariance prior energy prior model priori information probabilistic probability density Ptrue reconstruction reference potential regression function saddle point approximation sampled Section smoothness prior solution space specific prior stationarity equation statistical stochastic symmetric temperature template theory tion training data typically values vector zero

Popular passages

Page 392 - In G. Shafer and J. Pearl, editors, Readings in Uncertain Reasoning, pages 575-609.‎
Appears in 17 books from 1979-2003
Page 390 - K. Rose, E. Gurewitz, and GC Fox, "Statistical mechanics and phase transitions in clustering," Physical Review Letters, vol.‎
Appears in 29 books from 1991-2005
Page 383 - Bayesian non-linear modelling for the 1993 energy prediction competition. In G. Heidbreder, editor, Maximum Entropy and Bayesian Methods, Santa Barbara 1993, pages 221-234, Dordrecht, 1996.‎
Appears in 5 books from 1998-2003
Page 395 - WN Venables and BD Ripley, Modern Applied Statistics with S-Plus (Springer- Verlag, New York, 1994).‎
Appears in 12 books from 1974-2003

References to this book

About the author (2003)

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.

Bibliographic information

TitleBayesian Field Theory
Bayesian Field Theory
AuthorJörg C. Lemm
Editionillustrated
PublisherJHU Press, 2003
ISBN0801872200, 9780801872204
Length432 pages
  
Export CitationBiBTeX EndNote RefMan