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.

This monograph examines the problem of recovering and processing information when the underlying data are limited or partial, and the corresponding models that form the basis for estimation and inference are ill-posed or undermined

Information and Entropy Econometrics - A Review and Synthesis summarizes the basics of information theoretic methods in econometrics and the connecting theme among these methods. The sub-class of methods that treat the observed sample moments as stochastic is discussed in greater details. I Information and Entropy Econometrics - A Review and Synthesis -focuses on inter-connection between information theory, estimation and inference. -provides a detailed survey of information theoretic concepts and quantities used within econometrics and then show how these quantities are used within IEE. -pays special attention for the interpretation of these quantities and for describing the relationships between information theoretic estimators and traditional estimators. Readers need a basic knowledge of econometrics, but do not need prior knowledge of information theory. The survey is self contained and interested readers can replicate all results and examples provided. Whenever necessary the readers are referred to the relevant literature. Information and Entropy Econometrics - A Review and Synthesis will benefit researchers looking for a concise introduction to the basics of IEE and to acquire the basic tools necessary for using and understanding these methods. Applied researchers can use the book to learn improved new methods, and applications for extracting information from noisy and limited data and for learning from these data.

Articles on econometric methodology with special reference to the quantification of poverty and economic inequality are presented in this book. Poverty and inequality measurement present special problems to the econometrician, and most of these papers analyze how to attack those problems. The topics and contributions in the book are a very good representation of Camilo Dagum's astounding diversity of interests and overall eclecticism. Several of the authors are leading pioneers in econometric methodology. Several others are pioneers in economic theory and others are the leading applied economists in income distribution analysis in the world. The topics accurately reflect Camilo Dagum's breadth of understanding across varios economic sub-fields, all complex in nature.

This book uses a mathematical approach to deriving the laws of science and technology, based upon the concept of Fisher information. The approach that follows from these ideas is called the principle of Extreme Physical Information (EPI). The authors show how to use EPI to determine the theoretical input/output laws of unknown systems. Will benefit readers whose math skill is at the level of an undergraduate science or engineering degree.

Entropy Theory and its Application in Environmental and Water Engineering responds to the need for a book that deals with basic concepts of entropy theory from a hydrologic and water engineering perspective and then for a book that deals with applications of these concepts to a range of water engineering problems. The range of applications of entropy is constantly expanding and new areas finding a use for the theory are continually emerging. The applications of concepts and techniques vary across different subject areas and this book aims to relate them directly to practical problems of environmental and water engineering. The book presents and explains the Principle of Maximum Entropy (POME) and the Principle of Minimum Cross Entropy (POMCE) and their applications to different types of probability distributions. Spatial and inverse spatial entropy are important for urban planning and are presented with clarity. Maximum entropy spectral analysis and minimum cross entropy spectral analysis are powerful techniques for addressing a variety of problems faced by environmental and water scientists and engineers and are described here with illustrative examples. Giving a thorough introduction to the use of entropy to measure the unpredictability in environmental and water systems this book will add an essential statistical method to the toolkit of postgraduates, researchers and academic hydrologists, water resource managers, environmental scientists and engineers. It will also offer a valuable resource for professionals in the same areas, governmental organizations, private companies as well as students in earth sciences, civil and agricultural engineering, and agricultural and rangeland sciences. This book: Provides a thorough introduction to entropy for beginners and more experienced users Uses numerous examples to illustrate the applications of the theoretical principles Allows the reader to apply entropy theory to the solution of practical problems Assumes minimal existing mathematical knowledge Discusses the theory and its various aspects in both univariate and bivariate cases Covers newly expanding areas including neural networks from an entropy perspective and future developments.