Uncertainty Theory

Uncertainty Theory
Author: Baoding Liu
Publisher: Springer
Total Pages: 263
Release: 2007-09-14
Genre: Technology & Engineering
ISBN: 3540731652

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.

The Mathematics of the Uncertain

The Mathematics of the Uncertain
Author: Eduardo Gil
Publisher: Springer
Total Pages: 897
Release: 2018-02-28
Genre: Technology & Engineering
ISBN: 3319738488

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.

Do Dice Play God?

Do Dice Play God?
Author: Ian Stewart
Publisher: Profile Books
Total Pages: 292
Release: 2019-06-06
Genre: Mathematics
ISBN: 178283401X

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.

Uncertain Differential Equations

Uncertain Differential Equations
Author: Kai Yao
Publisher: Springer
Total Pages: 166
Release: 2016-08-29
Genre: Technology & Engineering
ISBN: 3662527294

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.

An Introduction to the Uncertainty Principle

An Introduction to the Uncertainty Principle
Author: Sundaram Thangavelu
Publisher: Springer Science & Business Media
Total Pages: 189
Release: 2012-12-06
Genre: Mathematics
ISBN: 0817681647

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.

Estimators for Uncertain Dynamic Systems

Estimators for Uncertain Dynamic Systems
Author: A.I. Matasov
Publisher: Springer Science & Business Media
Total Pages: 428
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 9401153221

When solving the control and design problems in aerospace and naval engi neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from mea surement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple mentation. For example, the dimension of these algorithms can be very high.

Uncertain Optimal Control

Uncertain Optimal Control
Author: Yuanguo Zhu
Publisher: Springer
Total Pages: 211
Release: 2018-08-29
Genre: Technology & Engineering
ISBN: 9811321345

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.

The Uncertain Reasoner's Companion

The Uncertain Reasoner's Companion
Author: J. B. Paris
Publisher: Cambridge University Press
Total Pages: 28
Release: 1994
Genre: Computers
ISBN: 9780521460897

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

Uncertainty

Uncertainty
Author: William Briggs
Publisher: Springer
Total Pages: 274
Release: 2016-07-15
Genre: Mathematics
ISBN: 3319397567

This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance." The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, such as out-of-the-box regression, cannot help in discovering cause. This new way of looking at uncertainty ties together disparate fields — probability, physics, biology, the “soft” sciences, computer science — because each aims at discovering cause (of effects). It broadens the understanding beyond frequentist and Bayesian methods to propose a Third Way of modeling.

Understanding Uncertainty

Understanding Uncertainty
Author: Dennis V. Lindley
Publisher: John Wiley & Sons
Total Pages: 268
Release: 2006-08-28
Genre: Mathematics
ISBN: 0470055472

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.