Maximum Entropy and Bayesian Methods: Cambridge, England, 1988

ISBN-13: 9789048140442 / Angielski / Miękka / 2010 / 526 str.

John Skilling

Opis

This volume records the proceedings of the Fourteenth International Workshop on Maximum Entropy and Bayesian Methods, held in Cambridge, England from August 1-5, 1994. Throughout applied science, Bayesian inference is giving high quality results augmented with reliabilities in the form of probability values and probabilistic error bars. Maximum Entropy, with its emphasis on optimally selected results, is an important part of this. Across wide areas of spectroscopy and imagery, it is now realistic to generate clear results with quantified reliability. This power is underpinned with a foundation of solid mathematics. The annual Maximum Entropy Workshops have become the principal focus of developments in the field, and which capture the imaginative research that defines the state of the art in the subject. The breadth of application is seen in the thirty-three papers reproduced here, which are classified into subsections on Basics, Applications, Physics and Neural Networks. Audience: This volume will be of interest to graduate students and researchers whose work involves probability theory, neural networks, spectroscopic methods, statistical thermodynamics and image processing.

Spis treści

Tutorial.- Clearing up Mysteries — The Original Goal.- From Rationality and Consistency to Bayesian Probability.- Classic Maximum Entropy.- Developments in Maximum Entropy Data Analysis.- The Three Phases of Statistical Mechanics.- Bell’s Theorem. Inference and Quantum Transactions.- Philosophy.- Probability, Philosophy and Science: A briefing for Bayesians.- Statistical thermodynamics & Quantum mechanics.- The Statistics of Quantum Mechanical Wavefunctions.- Justification of the Maximum Entropy Criterion in Quantum Mechanics.- Approaches to Non-Equilibrium Statistical Mechanics.- Applications of Maximum Entropy to Condensed Matter Physics.- Problems of Maximum-Entropy Formalism in the Statistical Geometry of Simple Liquids.- Physical measurement techniques.- Liquid Structure Factor Determination by Neutron Scattering — Some Dangers of Maximum Entropy.- Quasielastic Neutron Scattering Data Evaluation Using the Maximum Entropy Method.- Maximum Entropy Reconstruction in Magnetic Resonance Imaging.- Solution of Autocorrelation Function Constrained Maximum Entropy Problems Using the Method of Simulated Annealing.- Solution of Laplace Transform Equations (Sum of Exponentials) by Maximum Entropy.- Maximum Entropy and Bayesian Approach in Tomographic Image Reconstruction and Restoration.- Crystallography.- Maximum-Entropy-Based Approaches to X-ray Structure Determination and Data Processing.- Maximum Entropy in Crystallography.- A Multisolution Phase Determination Method in X-Ray Crystallography.- The Challenge of X-RAY and Neutron Powder Diffraction.- A Statistical Potential for Modelling X-ray Electron Density Maps with Known Phases.- Chemical Spectroscopy.- Enhanced Information Recovery From Spectroscopic Data Using MaxEnt.- Bayesian Spectrum Analysis on Quadrature Nmr Data with Noise Correlations.- Selective Data-Sampling and Reconstruction of Phase Sensitive 2D NMR Spectra Using Maximum Entropy.- A New Maximum Entropy Processing Algorithm, with Applications to Nuclear Magnetic Resonance Experiments.- Sampling Strategies for Magnetic Resonance Experiments.- The Inverse Problem for Nuclear Magnetic Resonance.- Time series, Power spectra.- Maximum Entropy Calculations on a Discrete Probability Space: Predictions Confirmed.- Application of Classical, Bayesian and Maximum Entropy Spectrum Analysis to Nonstationary Time Series Data.- Identifying Discrete Cycles in Economic Data: Maximum Entropy Spectra and the Direct Fitting of Sinusoidal Functions.- Maximum Entropy Spectral Analysis of Hilbert Transformed Complex Data.- Astronomical techniques.- Maximum Entropy Tomography of Accretion Discs from Their Emission Lines.- Distances to Clusters of Galaxies Using Maximum Entropy.- The Application of Maximum Entropy Techniques to Chopped Astronomical Infrared Data.- Neural networks.- The Use of Bayesian and Entropic Methods in Neural Network Theory.- Electronic ‘Neural’ Nets for Solving Ill-Posed Problems with an Entropy Regulariser.- Fundamentals, Statistics.- Bayesian Model Selection: Examples Relevant to NMR.- Regularization and Inverse Problems.- Maximum Entropy and Inductive Inference.- Maximum Specific Entropy, Knowledge, Ordering, and Physical Measurements.- The Metrics Induced by the Kullback Number.- The Paradox of the Money Pump: A Resolution.- Constrained Maximum Entropy Methods in an Image Reconstruction Problem.- Entropy + Rain = Floods.- Maximum Entropy and Constrained Optimization.- The Eigenvalues of Mega-dimensional Matrices.- Bayesian Evaluation of Discrepant Experimental Data.- Superresolution limit for Signal recovery.- A Monotonic Property of Distributions Based on Entropy with Fractile Constraints.- Kinetic Theory and Ensembles of Maximum Entropy.- On the Use of Quadratic Regularisation within Maximum Entropy Image Restoration.- From Chirp to Chip, a Beginning.- Bayesian Data Analysis: Straight-line fitting.