Maximum Entropy and Bayesian Methods

ISBN-13: 9789401067928 / Angielski / Miękka / 2011 / 490 str.

P. F. Fougere

Opis

This volume represents the proceedings of the Ninth Annual MaxEnt Workshop, held at Dartmouth College in Hanover, New Hampshire, on August 14-18, 1989. These annual meetings are devoted to the theory and practice of Bayesian Probability and the Maximum Entropy Formalism. The fields of application exemplified at MaxEnt '89 are as diverse as the foundations of probability theory and atmospheric carbon variations, the 1987 Supernova and fundamental quantum mechanics. Subjects include sea floor drug absorption in man, pressures, neutron scattering, plasma equilibrium, nuclear magnetic resonance, radar and astrophysical image reconstruction, mass spectrometry, generalized parameter estimation, delay estimation, pattern recognition, heave responses in underwater sound and many others. The first ten papers are on probability theory, and are grouped together beginning with the most abstract followed by those on applications. The tenth paper involves both Bayesian and MaxEnt methods and serves as a bridge to the remaining papers which are devoted to Maximum Entropy theory and practice. Once again, an attempt has been made to start with the more theoretical papers and to follow them with more and more practical applications. Papers number 29, 30 and 31, by Kesaven, Seth and Kapur, represent a somewhat different, perhaps even "unorthodox" viewpoint, and are included here even though the editor and, indeed many in the audience at Dartmouth, disagreed with their content. I feel that scientific disagreements are essential in any developing field, and often lead to a deeper understanding.

Spis treści

Probability Theory as Logic.- Probability Theory and the Associativity Equation.- Objective Bayesianism and Geometry.- Consistency Principle for Data-Based Probabilistic Inference.- An Introduction to Parameter Estimation Using Bayesian Probability Theory.- From Laplace to Supernova Sn 1987A: Bayesian Inference in Astrophysics.- Atmospheric 14C Variations: A Bayesian Prospect.- On Decoupling Probability From Kinematics in Quantum Mechanics.- Bayesian Model Selection and Parameter Estimation Applied to Sea Floor Pressure Data.- Applications of Maximum Entropy and Bayesian Methods in Neutron Scattering.- The Conditional Entropy of a Canonical Constraint.- Solving Oversampled Data Problems by Maximum Entropy.- Constructing Priors in Maximum Entropy Methods.- Maximum Entropy With Nonlinear Constraints: Physical Examples.- Maximum Entropy Description of Plasma Equilibrium.- Linear Inversion by the Maximum Entropy Method With Specific Non-Trivial Prior Information.- Minimum Dissipation and Maximum Entropy.- Maximum Entropy and Equations of State for Random Cellular Structures.- Delay Estimation Using Maximum Entropy Derived Phase Information.- Drug Absorption in Man, and its Measurement by Maxent.- Quantified Maximum Entropy.- Quantified Maxent: An Nmr Application.- Maximum Entropy Reconstruction of Radar Cross-Section Images.- Fier: A Filtered Entropy Approach to Maximum Entropy Image Restoration.- Regularization in Coded Aperture Spect.- Burg Algorithm Applied to Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.- Maximum Entropy Analysis For Pattern Recognition.- Application Of Burg’S Spectral Analysis to Heave Response Modeling in Underwater Applications.- Maximum Entropy and Minimum Cross-Entropy Principles: Need For a Broader Perspective.- The Inverse Maxent and Minxent Principles and their Applications.- A Comparative Assessment of Entropic and Non-Entropic Methods of Estimation.- Maxent Applied to Linear Regression.