Mathematics Of Uncertainty

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Mathematics of Uncertainty

Author : Hans Bandemer
Publisher : Springer Science & Business Media
ISBN 13 : 3540284575
Total Pages : 199 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Mathematics of Uncertainty by : Hans Bandemer

Download or read book Mathematics of Uncertainty written by Hans Bandemer and published by Springer Science & Business Media. This book was released on 2006 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships. The notions of randomness and probability are examined as a model for the variability of observation and measurement results. Besides these basic ideas the book also presents methods of qualitative data analysis such as cluster analysis and classification, and of evaluation of functional relationships such as regression analysis and quantitative fuzzy data analysis.

Probability

Author : Dorian Feldman
Publisher : CRC Press
ISBN 13 : 9780824784522
Total Pages : 428 pages
Book Rating : 4.7/5 (845 download)

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Book Synopsis Probability by : Dorian Feldman

Download or read book Probability written by Dorian Feldman and published by CRC Press. This book was released on 1991-09-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uncertainty Theory

Author : Baoding Liu
Publisher : Springer
ISBN 13 : 3540731652
Total Pages : 255 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Uncertainty Theory by : Baoding Liu

Download or read book Uncertainty Theory written by Baoding Liu and published by Springer. This book was released on 2007-09-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.

Applications of Mathematics of Uncertainty

Author : John N. Mordeson
Publisher : Springer Nature
ISBN 13 : 3030869962
Total Pages : 307 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Applications of Mathematics of Uncertainty by : John N. Mordeson

Download or read book Applications of Mathematics of Uncertainty written by John N. Mordeson and published by Springer Nature. This book was released on 2021-11-17 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an examination of major problems facing the world using mathematics of uncertainty. These problems include climate change, coronavirus pandemic, human tracking, biodiversity, and other grand challenges. Mathematics of uncertainty is used in a modern more general sense than traditional mathematics. Since accurate data is impossible to obtain concerning human tracking and other global problems, mathematics of uncertainty is an ideal discipline to study these problems. The authors place several scientific studies into different mathematical settings such as nonstandard analysis and soft logic. Fuzzy differentiation is used to model the spread of diseases such as the coronavirus. The book uses fuzzy graph theory to examine the problems of human tracking and illegal immigration. The book is an excellent reference source for advanced under-graduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.

Do Dice Play God?

Author : Ian Stewart
Publisher : Profile Books
ISBN 13 : 178283401X
Total Pages : 292 pages
Book Rating : 4.7/5 (828 download)

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Book Synopsis Do Dice Play God? by : Ian Stewart

Download or read book Do Dice Play God? written by Ian Stewart and published by Profile Books. This book was released on 2019-06-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is everywhere. It lurks in every consideration of the future - the weather, the economy, the sex of an unborn child - even quantities we think that we know such as populations or the transit of the planets contain the possibility of error. It's no wonder that, throughout that history, we have attempted to produce rigidly defined areas of uncertainty - we prefer the surprise party to the surprise asteroid. We began our quest to make certain an uncertain world by reading omens in livers, tea leaves, and the stars. However, over the centuries, driven by curiosity, competition, and a desire be better gamblers, pioneering mathematicians and scientists began to reduce wild uncertainties to tame distributions of probability and statistical inferences. But, even as unknown unknowns became known unknowns, our pessimism made us believe that some problems were unsolvable and our intuition misled us. Worse, as we realized how omnipresent and varied uncertainty is, we encountered chaos, quantum mechanics, and the limitations of our predictive power. Bestselling author Professor Ian Stewart explores the history and mathematics of uncertainty. Touching on gambling, probability, statistics, financial and weather forecasts, censuses, medical studies, chaos, quantum physics, and climate, he makes one thing clear: a reasonable probability is the only certainty.

Probability and Statistics

Author : John Tabak
Publisher : Infobase Publishing
ISBN 13 : 0816068739
Total Pages : 241 pages
Book Rating : 4.8/5 (16 download)

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Book Synopsis Probability and Statistics by : John Tabak

Download or read book Probability and Statistics written by John Tabak and published by Infobase Publishing. This book was released on 2014-05-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a survey of the history and evolution of the branch of mathematics that focuses on probability and statistics, including useful applications and notable mathematicians in this area.

Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems

Author : Chakraverty, S.
Publisher : IGI Global
ISBN 13 : 1466649925
Total Pages : 442 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems by : Chakraverty, S.

Download or read book Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems written by Chakraverty, S. and published by IGI Global. This book was released on 2014-01-31 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.

Mathematics of Uncertainty for Coping with World Challenges

Author : John N. Mordeson
Publisher : Springer Nature
ISBN 13 : 3030686841
Total Pages : 209 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematics of Uncertainty for Coping with World Challenges by : John N. Mordeson

Download or read book Mathematics of Uncertainty for Coping with World Challenges written by John N. Mordeson and published by Springer Nature. This book was released on 2021-02-23 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book ranks countries with respect to their achievement of the Sustainable Development Goals and their vulnerability to climate change. Human livelihoods, stable economies, health, and high quality of life all depend on a stable climate and earth system, and a diversity of species and ecosystems. Climate change significantly impacts human trafficking, modern slavery, and global hunger. This book examines these global problems using techniques from mathematics of uncertainty. Since accurate data concerning human trafficking and modern slavery is impossible to obtain, mathematics of uncertainty is an ideal discipline to study these problems. The book also considers the interconnection between climate change, world hunger, human trafficking, modern slavery, and the coronavirus. Connectivity properties of fuzzy graphs are used to examine trafficking flow between regions in the world. The book is an excellent reference source for advanced undergraduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.

Fuzzy Data Analysis

Author : Hans Bandemer
Publisher : Springer Science & Business Media
ISBN 13 : 9401125066
Total Pages : 351 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Fuzzy Data Analysis by : Hans Bandemer

Download or read book Fuzzy Data Analysis written by Hans Bandemer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers. Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.

Uncertainty Theory

Author : Baoding Liu
Publisher : Springer Science & Business Media
ISBN 13 : 3642139582
Total Pages : 350 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Uncertainty Theory by : Baoding Liu

Download or read book Uncertainty Theory written by Baoding Liu and published by Springer Science & Business Media. This book was released on 2011-11-07 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Uncertainty is any concept that satisfies the axioms of uncertainty theory. Thus uncertainty is neither randomness nor fuzziness. It is also known from some surveys that a lot of phenomena do behave like uncertainty. How do we model uncertainty? How do we use uncertainty theory? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory, including uncertain programming, uncertain risk analysis, uncertain reliability analysis, uncertain process, uncertain calculus, uncertain differential equation, uncertain logic, uncertain entailment, and uncertain inference. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, system science, industrial engineering, computer science, artificial intelligence, finance, control, and management science will find this work a stimulating and useful reference.

Principles of Uncertainty

Author : Joseph B. Kadane
Publisher : CRC Press
ISBN 13 : 1351683365
Total Pages : 525 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Principles of Uncertainty by : Joseph B. Kadane

Download or read book Principles of Uncertainty written by Joseph B. Kadane and published by CRC Press. This book was released on 2020-11-25 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the first edition: Principles of Uncertainty is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. ... the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. ... A must-read for sure!—Christian Robert, CHANCE It's a lovely book, one that I hope will be widely adopted as a course textbook. —Michael Jordan, University of California, Berkeley, USA Like the prize-winning first edition, Principles of Uncertainty, Second Edition is an accessible, comprehensive text on the theory of Bayesian Statistics written in an appealing, inviting style, and packed with interesting examples. It presents an introduction to the subjective Bayesian approach which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. This new edition has been updated throughout and features new material on Nonparametric Bayesian Methods, the Dirichlet distribution, a simple proof of the central limit theorem, and new problems. Key Features: First edition won the 2011 DeGroot Prize Well-written introduction to theory of Bayesian statistics Each of the introductory chapters begins by introducing one new concept or assumption Uses "just-in-time mathematics"—the introduction to mathematical ideas just before they are applied

Measurement Uncertainty

Author : Simona Salicone
Publisher : Springer Science & Business Media
ISBN 13 : 0387463283
Total Pages : 235 pages
Book Rating : 4.3/5 (874 download)

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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 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.

Sustainable Development Goals: Analysis by Mathematics of Uncertainty

Author : John N. Mordeson
Publisher : Springer Nature
ISBN 13 : 3030485234
Total Pages : 237 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Sustainable Development Goals: Analysis by Mathematics of Uncertainty by : John N. Mordeson

Download or read book Sustainable Development Goals: Analysis by Mathematics of Uncertainty written by John N. Mordeson and published by Springer Nature. This book was released on 2020-06-22 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses mathematics of uncertainty to examine how well countries are achieving the 17 Sustainable Development Goals (SDGs) set by the members of the United Nations, with a focus on climate change, human trafficking and modern slavery. Although this approach has never been used before, mathematics of uncertainty is well suited to exploring these topics due to the lack of accurate data available. The authors place several scientific studies in a mathematical setting to pave the way for future research on issues of sustainability, climate change, human trafficking and modern slavery to using a wide range of mathematical techniques. Moreover, the book ranks countries in terms of their achievement of not only the SDGs, but in particular those SDGs pertinent to climate change, human trafficking, and modern slavery, and highlights the deficiencies in the foster care system that lead to human trafficking. As such it is an excellent reference resource for advanced undergraduate and graduate students in mathematics and the social sciences, as well as for researchers and teachers.

Modeling and Inverse Problems in the Presence of Uncertainty

Author : H. T. Banks
Publisher : CRC Press
ISBN 13 : 1482206439
Total Pages : 403 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Modeling and Inverse Problems in the Presence of Uncertainty by : H. T. Banks

Download or read book Modeling and Inverse Problems in the Presence of Uncertainty written by H. T. Banks and published by CRC Press. This book was released on 2014-04-01 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation i

Understanding Uncertainty

Author : Dennis V. Lindley
Publisher : John Wiley & Sons
ISBN 13 : 0470055472
Total Pages : 268 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Understanding Uncertainty by : Dennis V. Lindley

Download or read book Understanding Uncertainty written by Dennis V. Lindley and published by John Wiley & Sons. This book was released on 2006-08-28 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lively and informal introduction to the role of uncertainty and probability in people's lives from an everyday perspective From television game shows and gambling techniques to weather forecasting and the financial markets, virtually every aspect of modern life involves situations in which the outcomes are uncertain and of varying qualities. But as noted statistician Dennis Lindley writes in this distinctive text, "We want you to face up to uncertainty, not hide it away under false concepts, but to understand it and, moreover, to use the recent discoveries so that you can act in the face of uncertainty more sensibly than would have been possible without the skill." Accessibly written at an elementary level, this outstanding text examines uncertainty in various everyday situations and introduces readers to three rules--craftily laid out in the book--that prove uncertainty can be handled with as much confidence as ordinary logic. Combining a concept of utility with probability, the book insightfully demonstrates how uncertainty can be measured and used in everyday life, especially in decision-making and science. With a focus on understanding and using probability calculations, Understanding Uncertainty demystifies probability and: * Explains in straightforward detail the logic of uncertainty, its truths, and its falsehoods * Explores what has been learned in the twentieth century about uncertainty * Provides a logical, sensible method for acting in the face of uncertainty * Presents vignettes of great discoveries made in the twentieth century * Shows readers how to discern if another person--whether a lawyer, politician, scientist, or journalist--is talking sense, posing the right questions, or obtaining sound answers Requiring only a basic understanding of mathematical concepts and operations, Understanding Uncertainty is useful as a text for all students who have probability or statistics as part of their course, even at the most introductory level.

Do Dice Play God?

Author : Ian Stewart
Publisher : Basic Books
ISBN 13 : 1541699467
Total Pages : 304 pages
Book Rating : 4.5/5 (416 download)

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Book Synopsis Do Dice Play God? by : Ian Stewart

Download or read book Do Dice Play God? written by Ian Stewart and published by Basic Books. This book was released on 2019-09-03 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: A celebrated mathematician explores how math helps us make sense of the unpredictable We would like to believe we can know things for certain. We want to be able to figure out who will win an election, if the stock market will crash, or if a suspect definitely committed a crime. But the odds are not in our favor. Life is full of uncertainty --- indeed, scientific advances indicate that the universe might be fundamentally inexact --- and humans are terrible at guessing. When asked to predict the outcome of a chance event, we are almost always wrong. Thankfully, there is hope. As award-winning mathematician Ian Stewart reveals, over the course of history, mathematics has given us some of the tools we need to better manage the uncertainty that pervades our lives. From forecasting, to medical research, to figuring out how to win Let's Make a Deal, Do Dice Play God? is a surprising and satisfying tour of what we can know, and what we never will.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author : Luis Tenorio
Publisher : SIAM
ISBN 13 : 1611974917
Total Pages : 275 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio

Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by SIAM. This book was released on 2017-07-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.