A Theory Of Conditional Information For Probabilistic Inference In Intelligent Systems 1 Interval Of Events Approach

This paper emphasizes the need to develop further probability theory at the service of probabilistic intelligent systems. In the field of probabilistic systems, the causal relationships among variables of interest are viewed as if-then (or production) rules whose certainty factors are quantified as conditional probabilities. With some additional assumptions about the variables of interest, such as conditional independence, standard probability theory can be applied to carry out the reasoning processes. In more general situations, in which all information (in the premises as well as the conclusions) is in unconditional and conditional form-or in only conditional form-current probabilistic machinery requires more development to cope with this new situation. After identifying typical situations, we present a theory of conditional information in the form of the new concept of 'conditional events, ' compatible with all conditional probability quantifications. We specify applications of this theory to various problems in intelligent systems. The approach taken here to conditional events is through intervals of events. Applied research, Basic research, Command, Control and Communications.

This paper concludes the work begun in Part 1 in presenting a coherent theory of conditioning consistent with all conditional probability evaluations.

This is the sixth volume in the series "Mathematics in Industrial Prob lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subse quent discussions. Each chapter is devoted to one of the talks and is self contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to Thomas Hoffend (3M), John Spence (Eastman Kodak Company), Marius Orlowski (Mo torola, Inc. ), Robert J.

Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitable for graduate students.

This book constitutes the thoroughly refereed postproceedings of the International Workshop on Conditionals, Information, and Inference, WCII 2002, held in Hagen, Germany in May 2002. The 9 revised full papers presented together with 3 invited papers by leading researchers in the area were carefully selected during iterated rounds of reviewing and improvement. The papers address all current issues of research on conditionals, ranging from foundational, theoretical, and methodological aspects to applications in various contexts of knowledge representation.

This book provides the ultimate goal of economic studies to predict how the economy develops—and what will happen if we implement different policies. To be able to do that, we need to have a good understanding of what causes what in economics. Prediction and causality in economics are the main topics of this book's chapters; they use both more traditional and more innovative techniques—including quantum ideas -- to make predictions about the world economy (international trade, exchange rates), about a country's economy (gross domestic product, stock index, inflation rate), and about individual enterprises, banks, and micro-finance institutions: their future performance (including the risk of bankruptcy), their stock prices, and their liquidity. Several papers study how COVID-19 has influenced the world economy. This book helps practitioners and researchers to learn more about prediction and causality in economics -- and to further develop this important research direction.

Recent advances in the area of lifted inference, which exploits the structure inherent in relational probabilistic models. Statistical relational AI (StaRAI) studies the integration of reasoning under uncertainty with reasoning about individuals and relations. The representations used are often called relational probabilistic models. Lifted inference is about how to exploit the structure inherent in relational probabilistic models, either in the way they are expressed or by extracting structure from observations. This book covers recent significant advances in the area of lifted inference, providing a unifying introduction to this very active field. After providing necessary background on probabilistic graphical models, relational probabilistic models, and learning inside these models, the book turns to lifted inference, first covering exact inference and then approximate inference. In addition, the book considers the theory of liftability and acting in relational domains, which allows the connection of learning and reasoning in relational domains.