This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.

The Twelfth International Workshop on Maximum Entropy and Bayesian Methods in Sciences and Engineering (MaxEnt 92) was held in Paris, France, at the Centre National de la Recherche Scientifique (CNRS), July 19-24, 1992. It is important to note that, since its creation in 1980 by some of the researchers of the physics department at the Wyoming University in Laramie, this was the second time that it took place in Europe, the first time was in 1988 in Cambridge. The two specificities of MaxEnt workshops are their spontaneous and informal charac ters which give the participants the possibility to discuss easily and to make very fruitful scientific and friendship relations among each others. This year's organizers had fixed two main objectives: i) to have more participants from the European countries, and ii) to give special interest to maximum entropy and Bayesian methods in signal and image processing. We are happy to see that we achieved these objectives: i) we had about 100 participants with more than 50 per cent from the European coun tries, ii) we received many papers in the signal and image processing subjects and we could dedicate a full day of the workshop to the image modelling, restoration and recon struction problems.

Proceedings of the Thirteenth International Workshop on Maximum Entropy and Bayesian Methods

Proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods, Santa Fe, New Mexico, USA, 1995

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.

The 10th International Workshop on Maximum Entropy and Bayesian Methods, MaxEnt 90, was held in Laramie, Wyoming from 30 July to 3 August 1990. This volume contains the scientific presentations given at that meeting. This series of workshops originated in Laramie in 1981, where the first three of what were to become annual workshops were held. The fourth meeting was held in Calgary. the fifth in Laramie, the sixth and seventh in Seattle, the eighth in Cambridge, England, and the ninth at Hanover, New Hampshire. It is most appropriate that the tenth workshop, occurring in the centennial year of Wyoming's statehood, was once again held in Laramie. The original purpose of these workshops was twofold. The first was to bring together workers from diverse fields of scientific research who individually had been using either some form of the maximum entropy method for treating ill-posed problems or the more general Bayesian analysis, but who, because of the narrow focus that intra-disciplinary work tends to impose upon most of us, might be unaware of progress being made by others using these same techniques in other areas. The second was to introduce to those who were somewhat aware of maximum entropy and Bayesian analysis and wanted to learn more, the foundations, the gestalt, and the power of these analyses. To further the first of these ends, presenters at these workshops have included workers from area. s as varied as astronomy, economics, environmenta.

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.

This volume has its origin in the Seventeenth International Workshop on Maximum Entropy and Bayesian Methods, MAXENT 97. The workshop was held at Boise State University in Boise, Idaho, on August 4 -8, 1997. As in the past, the purpose of the workshop was to bring together researchers in different fields to present papers on applications of Bayesian methods (these include maximum entropy) in science, engineering, medicine, economics, and many other disciplines. Thanks to significant theoretical advances and the personal computer, much progress has been made since our first Workshop in 1981. As indicated by several papers in these proceedings, the subject has matured to a stage in which computational algorithms are the objects of interest, the thrust being on feasibility, efficiency and innovation. Though applications are proliferating at a staggering rate, some in areas that hardly existed a decade ago, it is pleasing that due attention is still being paid to foundations of the subject. The following list of descriptors, applicable to papers in this volume, gives a sense of its contents: deconvolution, inverse problems, instrument (point-spread) function, model comparison, multi sensor data fusion, image processing, tomography, reconstruction, deformable models, pattern recognition, classification and group analysis, segmentation/edge detection, brain shape, marginalization, algorithms, complexity, Ockham's razor as an inference tool, foundations of probability theory, symmetry, history of probability theory and computability. MAXENT 97 and these proceedings could not have been brought to final form without the support and help of a number of people.

This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.

In 1978 Edwin T. Jaynes and Myron Tribus initiated a series of workshops to exchange ideas and recent developments in technical aspects and applications of Bayesian probability theory. The first workshop was held at the University of Wyoming in 1981 organized by C.R. Smith and W.T. Grandy. Due to its success, the workshop was held annually during the last 18 years. Over the years, the emphasis of the workshop shifted gradually from fundamental concepts of Bayesian probability theory to increasingly realistic and challenging applications. The 18th international workshop on Maximum Entropy and Bayesian Methods was held in Garching / Munich (Germany) (27-31. July 1998). Opening lectures by G. Larry Bretthorst and by Myron Tribus were dedicated to one of th the pioneers of Bayesian probability theory who died on the 30 of April 1998: Edwin Thompson Jaynes. Jaynes revealed and advocated the correct meaning of 'probability' as the state of knowledge rather than a physical property. This inter pretation allowed him to unravel longstanding mysteries and paradoxes. Bayesian probability theory, "the logic of science" - as E.T. Jaynes called it - provides the framework to make the best possible scientific inference given all available exper imental and theoretical information. We gratefully acknowledge the efforts of Tribus and Bretthorst in commemorating the outstanding contributions of E.T. Jaynes to the development of probability theory.