Maximum Entropy and Bayesian Methods

Bayesian probability theory and maximum entropy methods are at the core of a new view of scientific inference. These new' ideas, along with the revolution in computational methods afforded by modern computers, allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. This volume records the Proceedings of Eleventh Annual Maximum Entropy' Workshop, held at Seattle University in June, 1991. These workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this volume. There are tutorial papers, theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. The contributions contained in this volume present a state-of-the-art review that will be influential and useful for many years to come.

Inhalt
The Gibbs Paradox.- Bayesian Solution of Ordinary Differential Equations.- Bayesian Interpolation.- Estimating the Ratio of Two Amplitudes in Nuclear Magnetic Resonance Data.- A Bayesian Method for the Detection of a Periodic Signal of Unknown Shape and Period.- Linking the Plausible and Demonstrative Inferences.- Dimensional Analysis in Data Modeling.- Entropies of Likelihood Functions.- Maximum Likelihood Estimation of the Lagrange Parameters of the Maximum Entropy Distributions.- Entropy of Form and Hierarchic Organization.- A Bayesian Looks at the Anthropic Principle.- The Evidence for Neutral Networks.- Unmixing Mineral Spectra Using a Neural Net with Maximum Entropy Regularization.- Bayesian Mixture Modeling.- Point-Process Theory and the Surveillance of Many Objects.- A Matlab Program to Calculate the Maximum Entropy Distributions.- Memsys as Debugger.- Entropy and Sunspots: Their Bearing on Time-Series.- Basic Concepts in Multisensor Data Fusion.- Combining Data from Different Experiments: Bayesian Analysis and Meta-Analysis.- Modelling Drug Behaviour in the Body with Maxent.- Information Entropy and Dose-Response Functions for Risk Analysis.- Making Binary Decisions Based on the Posterior Probability Distribution Associated with Tomographic Reconstructions.- The Application of Maxent to Electrospray Mass Spectrometry.- The Application of Maxent to Electron Microscopy.- The Inference of Physical Phenomena in Chemistry: Abstract Tomography, Gedanken Experiments, and Surprisal Analysis.- The Maximum Entropy Reconstruction of Patterson and Fourier Densities in Orientationally Disordered Molecular Crystals: A Systematic Test for Crystallographic Interpolation Models.- On a Bayesian Approach to Coherent Radar Imaging.- Application of Maximum Entropy to Radio Imagingof Geological Features.- Deterministic Signals in Height of Sea Level Worldwide.- The Grand Canonical Sampler for Bayesian Integration.- Recent Developments in Information-Theoretic Statistical Analysis.- Murphy's Law and Noninformative Priors.- A Scientific Concept of Probability.- Bayesian Logic and Statistical Mechanics Illustrated by a Quantum Spin 1/2 Ensemble.