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.
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 430 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.
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.
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 235 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.
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.
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 141 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.
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.
Download or read book The Emergence of Probability written by Ian Hacking and published by Cambridge University Press. This book was released on 1984-06-21 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes an introduction, contextualizing his book in light of developing philosophical trends.
Download or read book Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2005-02-25 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.
Download or read book Game Theoretic Foundations for Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2019-03-21 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University
Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Download or read book Does Mathematical Study Develop Logical Thinking Testing The Theory Of Formal Discipline written by Matthew Inglis and published by World Scientific. This book was released on 2016-09-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results.Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents.Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy.
Download or read book System Modelling and Optimization written by J. Dolezal and published by Springer. This book was released on 2013-06-05 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings volume contains carefully selected papers presented during the 17th IFIP Conference on System Modelling and Optimization. Optimization theory and practice, optimal control, system modelling, stochastic optimization, and technical and non-technical applications of the existing theory are among areas mostly addressed in the included papers. Main directions are treated in addition to several survey papers based on invited presentations of leading specialists in the respective fields. Publication provides state-of-the-art in the area of system theory and optimization and points out several new areas (e.g fuzzy set, neural nets), where classical optimization topics intersects with computer science methodology.
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.
Download or read book The Probability of God written by Dr. Stephen D. Unwin and published by Forum Books. This book was released on 2004-10-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Does God exist? This is probably the most debated question in the history of mankind. Scholars, scientists, and philosophers have spent their lifetimes trying to prove or disprove the existence of God, only to have their theories crucified by other scholars, scientists, and philosophers. Where the debate breaks down is in the ambiguities and colloquialisms of language. But, by using a universal, unambiguous language—namely, mathematics—can this question finally be answered definitively? That’s what Dr. Stephen Unwin attempts to do in this riveting, accessible, and witty book, The Probability of God. At its core, this groundbreaking book reveals how a math equation developed more than 200 years ago by noted European philosopher Thomas Bayes can be used to calculate the probability that God exists. The equation itself is much more complicated than a simple coin toss (heads, He’s up there running the show; tails, He’s not). Yet Dr. Unwin writes with a clarity that makes his mathematical proof easy for even the nonmathematician to understand and a verve that makes his book a delight to read. Leading you carefully through each step in his argument, he demonstrates in the end that God does indeed exist. Whether you’re a devout believer and agree with Dr. Unwin’s proof or are unsure about all things divine, you will find this provocative book enlightening and engaging. “One of the most innovative works [in the science and religion movement] is The Probability of God...An entertaining exercise in thinking.”—Michael Shermer, Scientific American “Unwin’s book [is] peppered with wry, self-deprecating humor that makes the scientific discussions more accessible...Spiritually inspiring.”--Chicago Sun Times “A pleasantly breezy account of some complicated matters well worth learning about.”--Philadelphia Inquirer “One of the best things about the book is its humor.”--Cleveland Plain Dealer “In a book that is surprisingly lighthearted and funny, Unwin manages to pack in a lot of facts about science and philosophy.”--Salt Lake Tribune
Download or read book Probability Theory written by and published by Allied Publishers. This book was released on 2013 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory
Download or read book What s Happening in the Mathematical Sciences written by Barry Cipra and published by American Mathematical Soc.. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.
