Probabilistic Analysis Of Belief Functions

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Probabilistic Analysis of Belief Functions

Author : Ivan Kramosil
Publisher : Springer Science & Business Media
ISBN 13 : 9780306467028
Total Pages : 236 pages
Book Rating : 4.4/5 (67 download)

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Book Synopsis Probabilistic Analysis of Belief Functions by : Ivan Kramosil

Download or read book Probabilistic Analysis of Belief Functions written by Ivan Kramosil and published by Springer Science & Business Media. This book was released on 2001-12-31 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the eternal beauty and truth of the laws governing the run of stars on heavens over his head, and spurred by the idea to catch, perhaps for the smallest fraction of the shortest instant, the Eternity itself, man created such masterpieces of human intellect like the Platon's world of ideas manifesting eternal truths, like the Euclidean geometry, or like the Newtonian celestial me chanics. However, turning his look to the sub-lunar world of our everyday efforts, troubles, sorrows and, from time to time but very, very seldom, also our successes, he saw nothing else than a world full of uncertainty and tem porariness. One remedy or rather consolation was that of the deep and sage resignation offered by Socrates: I know, that I know nothing. But, happy or unhappy enough, the temptation to see and to touch at least a very small por tion of eternal truth also under these circumstances and behind phenomena charged by uncertainty was too strong. Probability theory in its most sim ple elementary setting entered the scene. It happened in the same, 17th and 18th centuries, when celestial mechanics with its classical Platonist paradigma achieved its greatest triumphs. The origins of probability theory were inspired by games of chance like roulettes, lotteries, dices, urn schemata, etc. and probability values were simply defined by the ratio of successful or winning results relative to the total number of possible outcomes.

Classic Works of the Dempster-Shafer Theory of Belief Functions

Author : Ronald R. Yager
Publisher : Springer
ISBN 13 : 354044792X
Total Pages : 813 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Classic Works of the Dempster-Shafer Theory of Belief Functions by : Ronald R. Yager

Download or read book Classic Works of the Dempster-Shafer Theory of Belief Functions written by Ronald R. Yager and published by Springer. This book was released on 2008-01-22 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management. The book includes a foreword reflecting the development of the theory in the last forty years.

Probabilistic Analysis of Belief Functions

Author : Ivan Kramosil
Publisher : Springer Science & Business Media
ISBN 13 : 1461505879
Total Pages : 222 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Probabilistic Analysis of Belief Functions by : Ivan Kramosil

Download or read book Probabilistic Analysis of Belief Functions written by Ivan Kramosil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the eternal beauty and truth of the laws governing the run of stars on heavens over his head, and spurred by the idea to catch, perhaps for the smallest fraction of the shortest instant, the Eternity itself, man created such masterpieces of human intellect like the Platon's world of ideas manifesting eternal truths, like the Euclidean geometry, or like the Newtonian celestial me chanics. However, turning his look to the sub-lunar world of our everyday efforts, troubles, sorrows and, from time to time but very, very seldom, also our successes, he saw nothing else than a world full of uncertainty and tem porariness. One remedy or rather consolation was that of the deep and sage resignation offered by Socrates: I know, that I know nothing. But, happy or unhappy enough, the temptation to see and to touch at least a very small por tion of eternal truth also under these circumstances and behind phenomena charged by uncertainty was too strong. Probability theory in its most sim ple elementary setting entered the scene. It happened in the same, 17th and 18th centuries, when celestial mechanics with its classical Platonist paradigma achieved its greatest triumphs. The origins of probability theory were inspired by games of chance like roulettes, lotteries, dices, urn schemata, etc. and probability values were simply defined by the ratio of successful or winning results relative to the total number of possible outcomes.

Decision Analysis Using Belief Functions

Author : SRI International. Artificial Intelligence Center
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (221 download)

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Book Synopsis Decision Analysis Using Belief Functions by : SRI International. Artificial Intelligence Center

Download or read book Decision Analysis Using Belief Functions written by SRI International. Artificial Intelligence Center and published by . This book was released on 1989 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that it yields expected values identical to those obtained by a probabilistic analysis that makes the same assumption. We maintain a strict separation between evidence that carries information about a situation and assumptions that may be made for disambiguation of choices. In addition, we show how the decision analysis methodology frequently employed in probabilistic reasoning can be extended for use with belief functions. This generalization of decision analysis allows the use of belief functions within the familiar framework of decision trees."

A Mathematical Theory of Evidence

Author : Glenn Shafer
Publisher : Princeton University Press
ISBN 13 : 0691214697
Total Pages : pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis A Mathematical Theory of Evidence by : Glenn Shafer

Download or read book A Mathematical Theory of Evidence written by Glenn Shafer and published by Princeton University Press. This book was released on 2020-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.

The Geometry of Uncertainty

Author : Fabio Cuzzolin
Publisher : Springer Nature
ISBN 13 : 3030631532
Total Pages : 850 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis The Geometry of Uncertainty by : Fabio Cuzzolin

Download or read book The Geometry of Uncertainty written by Fabio Cuzzolin and published by Springer Nature. This book was released on 2020-12-17 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.

Philosophy of Probability

Author : J.P. Dubucs
Publisher : Springer Science & Business Media
ISBN 13 : 9401582084
Total Pages : 304 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Philosophy of Probability by : J.P. Dubucs

Download or read book Philosophy of Probability written by J.P. Dubucs and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophy of Probability provides a comprehensive introduction to theoretical issues that occupy a central position in disciplines ranging from philosophy of mind and epistemology to cognitive science, decision theory and artificial intelligence. Some contributions shed new light on the standard conceptions of probability (Bayesianism, logical and computational theories); others offer detailed analyses of two important topics in the field of cognitive science: the meaning and the representation of (partial) belief, and the management of uncertainty. The authors of this well-balanced account are philosophers as well as computer scientists (among them, L.J. Cohen, D. Miller, P. Gärdenfors, J. Vickers, D. Dubois and H. Prade). This multidisciplinary approach to probability is designed to illuminate the intricacies of the problems in the domain of cognitive inquiry. No one interested in epistemology or aritificial intelligence will want to miss it.

A novel decision probability transformation method based on belief interval

Author : Zhan Deng
Publisher : Infinite Study
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4./5 ( download)

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Book Synopsis A novel decision probability transformation method based on belief interval by : Zhan Deng

Download or read book A novel decision probability transformation method based on belief interval written by Zhan Deng and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Dempster–Shafer evidence theory, the basic probability assignment (BPA) can effectively represent and process uncertain information. How to transform the BPA of uncertain information into a decision probability remains a problem to be solved. In the light of this issue, we develop a novel decision probability transformation method to realize the transition from the belief decision to the probability decision in the framework of Dempster–Shafer evidence theory. The newly proposed method considers the transformation of BPA with multi-subset focal elements from the perspective of the belief interval, and applies the continuous interval argument ordered weighted average operator to quantify the data information contained in the belief interval for each singleton. Afterward, we present an approach to calculate the support degree of the singleton based on quantitative data information. According to the support degree of the singleton, the BPA of multi-subset focal elements is allocated reasonably. Furthermore, we introduce the concepts of probabilistic information content in this paper, which is utilized to evaluate the performance of the decision probability transformation method. Eventually, a few numerical examples and a practical application are given to demonstrate the rationality and accuracy of our proposed method.

Uncertainty in Artificial Intelligence

Author : L.N. Kanal
Publisher : Elsevier
ISBN 13 : 1483296520
Total Pages : 522 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Uncertainty in Artificial Intelligence by : L.N. Kanal

Download or read book Uncertainty in Artificial Intelligence written by L.N. Kanal and published by Elsevier. This book was released on 2014-06-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to deal with uncertainty is a subject of much controversy in Artificial Intelligence. This volume brings together a wide range of perspectives on uncertainty, many of the contributors being the principal proponents in the controversy.Some of the notable issues which emerge from these papers revolve around an interval-based calculus of uncertainty, the Dempster-Shafer Theory, and probability as the best numeric model for uncertainty. There remain strong dissenting opinions not only about probability but even about the utility of any numeric method in this context.

On The Validity of Dempster-Shafer Theory

Author : Jean Dezert
Publisher : Infinite Study
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4./5 ( download)

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Book Synopsis On The Validity of Dempster-Shafer Theory by : Jean Dezert

Download or read book On The Validity of Dempster-Shafer Theory written by Jean Dezert and published by Infinite Study. This book was released on 2012-11-01 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: We challenge the validity of Dempster-Shafer Theory by using an emblematic example to show that DS rule produces counter-intuitive result. Further analysis reveals that the result comes from a understanding of evidence pooling which goes against the common expectation of this process. Although DS theory has attracted some interest of the scientific community working in information fusion and artificial intelligence, its validity to solve practical problems is problematic, because it is not applicable to evidences combination in general, but only to a certain type situations which still need to be clearly identified.

Probabilistic Reasoning in Intelligent Systems

Author : Judea Pearl
Publisher : Elsevier
ISBN 13 : 0080514898
Total Pages : 573 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Probabilistic Reasoning in Intelligent Systems by : Judea Pearl

Download or read book Probabilistic Reasoning in Intelligent Systems written by Judea Pearl and published by Elsevier. This book was released on 2014-06-28 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Reasoning in Intelligent Systems is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty--and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition--in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Modelling Probabilistic and Logical Relations with Belief Functions

Author :
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Modelling Probabilistic and Logical Relations with Belief Functions by :

Download or read book Modelling Probabilistic and Logical Relations with Belief Functions written by and published by . This book was released on 1995 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The project aims to explore through a variety of implementations a paradigm for the analysis of scientific and operational phenomena that depend on formalizations of uncertainty through probabilistic models. Such models can be interpreted as representations of random processes, or they can be interpreted as representations of the uncertainty of an analyst facing a situation described by the model. These interpretations are often viewed as mutually exclusive, but we regard them as complementary, and hence simultaneously applicable. A major motivating reason for constructing the models is to facilitate making uncertain inferences, followed in many cases by decision making informed by the inferences. The central principle of probabilistic inference remains, as it has been for 200 years, the Bayesian principle of updating inferences by formal computation of conditional probabilities, that is, by conditioning on the stream of incoming data. The belief function principle is a relaxation of the Bayesian rule, first suggested in special cases by R.A. Fisher about 65 years ago under the name fiducial inference, that retains the feature of conditioning on the data but does not require the full specification of a priori probabilities for all eventualities represented by the model. For example, in the ubiquitous class of Gaussian linear models the Bayesian formulation relies on awkward "improper priors" that are artifacts, that is, do not specify meaningful uncertainty judgments, whereas the normal linear belief function model dispenses with such priors and proceeds directly to conditioning.

Degrees of Belief

Author : Franz Huber
Publisher : Springer Science & Business Media
ISBN 13 : 1402091982
Total Pages : 352 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Degrees of Belief by : Franz Huber

Download or read book Degrees of Belief written by Franz Huber and published by Springer Science & Business Media. This book was released on 2008-12-21 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This anthology is the first book to give a balanced overview of the competing theories of degrees of belief. It also explicitly relates these debates to more traditional concerns of the philosophy of language and mind and epistemic logic.

Soft Methods in Probability, Statistics and Data Analysis

Author : Przemyslaw Grzegorzewski
Publisher : Springer Science & Business Media
ISBN 13 : 3790817732
Total Pages : 376 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis Soft Methods in Probability, Statistics and Data Analysis by : Przemyslaw Grzegorzewski

Download or read book Soft Methods in Probability, Statistics and Data Analysis written by Przemyslaw Grzegorzewski and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.

Belief Functions: Theory and Applications

Author : Jiřina Vejnarová
Publisher : Springer
ISBN 13 : 3319455591
Total Pages : 255 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Belief Functions: Theory and Applications by : Jiřina Vejnarová

Download or read book Belief Functions: Theory and Applications written by Jiřina Vejnarová and published by Springer. This book was released on 2016-09-07 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the 4th International Conference on Belief Functions, BELIEF 2016, held in Prague, Czech Republic, in September 2016. The 25 revised full papers presented in this book were carefully selected and reviewed from 33 submissions. The papers describe recent developments of theoretical issues and applications in various areas such as combination rules; conflict management; generalized information theory; image processing; material sciences; navigation.

The Emergence of Probability

Author : Ian Hacking
Publisher : Cambridge University Press
ISBN 13 : 9780521685573
Total Pages : 260 pages
Book Rating : 4.6/5 (855 download)

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Book Synopsis The Emergence of Probability by : Ian Hacking

Download or read book The Emergence of Probability written by Ian Hacking and published by Cambridge University Press. This book was released on 2006-07-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends.

Information Fusion in Signal and Image Processing

Author : Isabelle Bloch
Publisher : John Wiley & Sons
ISBN 13 : 1118623851
Total Pages : 229 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Information Fusion in Signal and Image Processing by : Isabelle Bloch

Download or read book Information Fusion in Signal and Image Processing written by Isabelle Bloch and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of information fusion has grown considerably during the last few years, leading to a rapid and impressive evolution. In such fast-moving times, it is important to take stock of the changes that have occurred. As such, this books offers an overview of the general principles and specificities of information fusion in signal and image processing, as well as covering the main numerical methods (probabilistic approaches, fuzzy sets and possibility theory and belief functions).