The Mathematics Of The Uncertain

Author : Ian Stewart
Publisher : Basic Books
Page : 304 pages
File Size : 47,5 Mb
Release : 2019-09-03
Category : Mathematics
ISBN : 9781541699465

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Do Dice Play God? by Ian Stewart Pdf

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.

Author : Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil
Publisher : Springer
Page : 917 pages
File Size : 43,5 Mb
Release : 2018-02-28
Category : Technology & Engineering
ISBN : 9783319738482

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The Mathematics of the Uncertain by Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil Pdf

This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics), Mathematics of communication (Information Theory), and Mathematics of imprecision (Fuzzy Sets Theory and others). These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.

Author : Baoding Liu
Publisher : Springer
Page : 255 pages
File Size : 48,6 Mb
Release : 2007-09-14
Category : Technology & Engineering
ISBN : 9783540731658

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Uncertainty Theory by Baoding Liu Pdf

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.

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681647

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An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.

Author : J. B. Paris
Publisher : Cambridge University Press
Page : 28 pages
File Size : 45,6 Mb
Release : 1994
Category : Computers
ISBN : 0521460891

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The Uncertain Reasoner's Companion by J. B. Paris Pdf

This is an introduction to the mathematical foundations of uncertain reasoning.

Author : Hans Bandemer
Publisher : Springer
Page : 190 pages
File Size : 43,9 Mb
Release : 2008-01-25
Category : Technology & Engineering
ISBN : 9783540312284

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Mathematics of Uncertainty by Hans Bandemer Pdf

"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.

Author : J. B. Paris
Publisher : Cambridge University Press
Page : 224 pages
File Size : 48,6 Mb
Release : 1994
Category : Computers
ISBN : 9780521460897

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The Uncertain Reasoner's Companion by J. B. Paris Pdf

This is an introduction to the mathematical foundations of uncertain reasoning.

Author : T.J. Sullivan
Publisher : Springer
Page : 342 pages
File Size : 43,9 Mb
Release : 2015-12-14
Category : Mathematics
ISBN : 9783319233956

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Introduction to Uncertainty Quantification by T.J. Sullivan Pdf

This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.

Author : Joseph B. Kadane
Publisher : CRC Press
Page : 525 pages
File Size : 41,9 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781351683364

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Principles of Uncertainty by Joseph B. Kadane Pdf

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

Author : Ivan Hlavacek,Jan Chleboun,Ivo Babuska
Publisher : Elsevier
Page : 485 pages
File Size : 44,8 Mb
Release : 2004-12-09
Category : Science
ISBN : 9780080543376

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Uncertain Input Data Problems and the Worst Scenario Method by Ivan Hlavacek,Jan Chleboun,Ivo Babuska Pdf

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience. · Rigorous theory is established for the treatment of uncertainty in modeling· Uncertainty is considered in complex models based on partial differential equations or variational inequalities · Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more · Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present· Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form· Fairly self-contained book

Author : Michael J. Evans,Jeffrey S. Rosenthal
Publisher : WH Freeman
Page : 200 pages
File Size : 40,5 Mb
Release : 2010-03-01
Category : Mathematics
ISBN : 1429224630

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Probability and Statistics by Michael J. Evans,Jeffrey S. Rosenthal Pdf

Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor to the course, incorporating the computer and offering an integrated approach to inference that includes the frequency approach and the Bayesian inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout. Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. The new edition includes a number of features designed to make the material more accessible and level-appropriate to the students taking this course today.

Author : Kai Yao
Publisher : Springer
Page : 158 pages
File Size : 53,8 Mb
Release : 2016-08-29
Category : Technology & Engineering
ISBN : 9783662527290

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Uncertain Differential Equations by Kai Yao Pdf

This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

Author : Dennis V. Lindley
Publisher : John Wiley & Sons
Page : 434 pages
File Size : 46,6 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781118650233

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Understanding Uncertainty by Dennis V. Lindley Pdf

Praise for the First Edition "...a reference for everyone who is interested in knowing and handling uncertainty." —Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made. Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including: A critical study of transitivity, a basic concept in probability A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession A consideration of betting, showing that a bookmaker's odds are not expressions of probability Applications of the book’s thesis to statistics A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.

Author : Yuanguo Zhu
Publisher : Springer
Page : 208 pages
File Size : 55,8 Mb
Release : 2018-08-29
Category : Technology & Engineering
ISBN : 9789811321344

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Uncertain Optimal Control by Yuanguo Zhu Pdf

This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games. The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.

Author : Morris Kline
Publisher : Unknown
Page : 0 pages
File Size : 42,7 Mb
Release : 2009
Category : Mathematics
ISBN : 1435108477

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Mathematics, the Loss of Certainty by Morris Kline Pdf