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A Mathematical Theory Of Evidence
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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.
Book Synopsis A Mathematical Theory of Hints by : Juerg Kohlas
Download or read book A Mathematical Theory of Hints written by Juerg Kohlas and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: An approach to the modeling of and the reasoning under uncertainty. The book develops the Dempster-Shafer Theory with regard to the reliability of reasoning with uncertain arguments. Of particular interest here is the development of a new synthesis and the integration of logic and probability theory. The reader benefits from a new approach to uncertainty modeling which extends classical probability theory.
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 806 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.
Book Synopsis Measurement Uncertainty by : Simona Salicone
Download or read book Measurement Uncertainty written by Simona Salicone and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book’s unique approach.
Book Synopsis The Mathematical Theory of Black Holes by : Subrahmanyan Chandrasekhar
Download or read book The Mathematical Theory of Black Holes written by Subrahmanyan Chandrasekhar and published by Oxford University Press. This book was released on 1998 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing and working-out the entire subject matter. The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical concepts of space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident.
Book Synopsis Decision Making in Uncertain Situations by : Fabio Campos
Download or read book Decision Making in Uncertain Situations written by Fabio Campos and published by Universal-Publishers. This book was released on 2006 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main problem addressed by this work is how to model and combine bodies of knowledge (or evidence) while maintaining the representation of the unkowledge and of the conflict among the bodies. This is a problem with far-reaching applications in many knowledge segments, in particular for the fields of artificial intelligence, product design, decision making, knowledge engineering and uncertain probability. It must be kept in mind that knowledge based systems depend on algorithms able to relate the inputs of a system to a correct answer coming out of the knowledge-base, and both the inputs and the knowledge-base are subject to information imperfections caused by the unknowledge and the conflict. There are several formalism to deal with knowledge representation and combination, among them the Mathematical Theory of Evidence or Dempster-Shafer Theory. This work extends the Mathematical Theory of Evidence through the adoption of a new rule for the combination of evidence and a companion set of concepts. This extension solves the counter-intuitive problems illustrated in the original theory, extends its power of expression and allows the representation of uncertainty in the results. The representation of uncertainty implies the possibility of its use in decision-making and also makes explicit the relationship between the numeric results achieved and the results from classical probability theory.
Book Synopsis The Mathematical Theory of Communication by : Claude E Shannon
Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
Book Synopsis Mathematical Theory of Oil and Gas Recovery by : P. Bedrikovetsky
Download or read book Mathematical Theory of Oil and Gas Recovery written by P. Bedrikovetsky and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a pleasure to be asked to write the foreword to this interesting new book. When Professor Bedrikovetsky first accepted my invitation to spend an extended sabbatical period in the Department of Mineral Resources Engineering at Imperial College of Science, Technology and Medicine, I hoped it would be a period of fruitful collaboration. This book, a short course and a variety of technical papers are tangible evidence of a successful stay in the UK. I am also pleased that Professor Bedrikovetsky acted on my suggestion to publish this book with Kluwer as part of the petroleum publications for which I am Series Editor. The book derives much of its origin from the unpublished Doctor of Science thesis which Professor Bedrikovetsky prepared in Russian while at the Gubkin Institute. The original DSc contained a number of discrete publications unified by an analytical mathematics approach to fluid flow in petroleum reservoirs. During his sabbatical stay at Imperial College, Professor Bedrikovetsky has refined and extended many of the chapters and has discussed each one with internationally recognised experts in the field. He received great encouragement and editorial advice from Dr Gren Rowan, who pioneered analytical methods in reservoir modelling at BP for many years.
Book Synopsis An Introduction to the Theory of Surreal Numbers by : Harry Gonshor
Download or read book An Introduction to the Theory of Surreal Numbers written by Harry Gonshor and published by Cambridge University Press. This book was released on 1986-09-18 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
Book Synopsis The William Lowell Putnam Mathematical Competition 1985-2000 by : Kiran Sridhara Kedlaya
Download or read book The William Lowell Putnam Mathematical Competition 1985-2000 written by Kiran Sridhara Kedlaya and published by MAA. This book was released on 2002 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
Download or read book Set Theory written by John P. Burgess and published by Cambridge University Press. This book was released on 2022-03-10 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.
Book Synopsis Advances in the Dempster-Shafer Theory of Evidence by : Ronald R. Yager
Download or read book Advances in the Dempster-Shafer Theory of Evidence written by Ronald R. Yager and published by John Wiley & Sons. This book was released on 1994-03 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Builds on classical probability theory and offers an extremely workable solution to the many problems of artificial intelligence, concentrating on the rapidly growing areas of fuzzy reasoning and neural computing. Contains a collection of previously unpublished articles by leading researchers in the field.
Book Synopsis Mathematical Evolutionary Theory by : Marcus W. Feldman
Download or read book Mathematical Evolutionary Theory written by Marcus W. Feldman and published by . This book was released on 2014-07-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The papers in this volume celebrate Samuel Karlin's contributions to mathematical evolutionary theory."--Page vii.
Book Synopsis A Mathematical Theory of Hints by : Jürg Kohlas
Download or read book A Mathematical Theory of Hints written by Jürg Kohlas and published by . This book was released on 1871 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Mathematical Theory of Arguments for Statistical Evidence by : Paul-Andre Monney
Download or read book A Mathematical Theory of Arguments for Statistical Evidence written by Paul-Andre Monney and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the reasoning under uncertainty based on sta tistical evidence, where the word reasoning is taken to mean searching for arguments in favor or against particular hypotheses of interest. The kind of reasoning we are using is composed of two aspects. The first one is inspired from classical reasoning in formal logic, where deductions are made from a knowledge base of observed facts and formulas representing the domain spe cific knowledge. In this book, the facts are the statistical observations and the general knowledge is represented by an instance of a special kind of sta tistical models called functional models. The second aspect deals with the uncertainty under which the formal reasoning takes place. For this aspect, the theory of hints [27] is the appropriate tool. Basically, we assume that some uncertain perturbation takes a specific value and then logically eval uate the consequences of this assumption. The original uncertainty about the perturbation is then transferred to the consequences of the assumption. This kind of reasoning is called assumption-based reasoning. Before going into more details about the content of this book, it might be interesting to look briefly at the roots and origins of assumption-based reasoning in the statistical context. In 1930, R. A. Fisher [17] defined the notion of fiducial distribution as the result of a new form of argument, as opposed to the result of the older Bayesian argument.
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.
Book Synopsis On The Validity of Dempster's Rule of Combination of Evidence by : Lotfi A. Zadeh
Download or read book On The Validity of Dempster's Rule of Combination of Evidence written by Lotfi A. Zadeh and published by Infinite Study. This book was released on 1979-10-01 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a seminal paper published in 1967, Dempster has described a rule for combining independent sources of information. More recently, Dempster's rule has been employed as a basis for a mathematical theory of evidence. It is suggested in this note that there is a serious flaw in Dempster's rule which restricts its use in many applications.
