Lemm Bayesian Field Theory

Erscheinungsjahr 2003
ISBN: 978-0-8018-7797-1
Verlag: Johns Hopkins University Press
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 0 Seiten, Format (B × H): 156 mm x 235 mm

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.

Autoren/Hrsg.

Lemm, Jörg C.

Lemm, Jorg C.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein
• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

List of Figures
List of Tables
List of Numerical Case Studies
Acknowledgments
Part I: Introduction
Part II: Bayesian Framework
Chapter 1. Bayesian Models
Chapter 2. Bayesian Decision Theory
Chapter 3. A Priori Information
Part III: Gaussian Prior Factors
Chapter 4. Gaussian Prior Factor for Log-Likelihoods
Chapter 5. Gaussian Prior Factor For Likelihoods
Chapter 6. Quadratic Density Estimation and Empirical Risk Minimization
Chapter 7. Numerical Case Study: Density Estimation with Gaussian Specific Priors
Chapter 8. Gaussian Prior Factors for General Fields
Chapter 9. Covariances and Invariances
Chapter 10. Non-Zero Means
Chapter 11. Regression
Chapter 12. Classification
Part IV: Parameterizing Likelihoods: Variational Methods
Chapter 13. General Likelihood Parameterizations
Chapter 14. Gaussian Priors for Likelihood Parameterizations
Chapter 15. Linear Trial Spaces
Chapter 16. Linear Regression
Chapter 17. Mixture Models
Chapter 18. Additive Models
Chapter 19. Product Ansatz
Chapter 20. Decision Trees
Chapter 21. Projection Pursuit
Chapter 22. Neural Networks
Part V: Parameterizing Priors: Hyperparameters
Chapter 23. Quenched and Annealed Prior Normalization
Chapter 24. Saddle Point Approximations and Hyperparameters
Chapter 25. Adapting Prior Means
Chapter 26. Adapting Prior Covariances
Chapter 27. Integer Hyperparameters
Chapter 28. Hyperfields
Chapter 29. Auxiliary Fields
Chapter 30. Non-Quadratic Potentials
Part VI: Mixtures of Gaussian Prior Factors
Chapter 31. Multimodal Energy Surfaces
Chapter 32. Prior Mixtures for Density Estimation
Chapter 33. Numerical Case Study: Prior Mixtures for Density Estimation
Chapter 34. Prior Mixtures for Regression
Chapter 35. Local Mixtures
Chapter 36. Numerical Case Study: Image Completion
Part VII: Bayesian Inverse Quantum Theory (BIQT)
Chapter 37. Bayesian Inverse Quantum Statistics (BIQS)
Chapter 38. Bayesian Inverse Time-Dependent Quantum Theory (BITDQ)
Chapter 39. Bayesian Inverse Many-Body Theory
Part VIII: Summary
Bibliography
Index

Über Autor(innen)

Lemm, Jörg C.
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.