Introduction To Imprecise Probabilities

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Introduction to Imprecise Probabilities

Thomas Augustin,Frank P. A. Coolen,Gert de Cooman,Matthias C. M. Troffaes
Introduction to Imprecise Probabilities Book PDF

Author : Thomas Augustin,Frank P. A. Coolen,Gert de Cooman,Matthias C. M. Troffaes
Publisher : John Wiley & Sons
Page : 448 pages
File Size : 51,8 Mb
Release : 2014-04-11
Category : Mathematics
ISBN : 9781118763148

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Introduction to Imprecise Probabilities by Thomas Augustin,Frank P. A. Coolen,Gert de Cooman,Matthias C. M. Troffaes Pdf

In recent years, the theory has become widely accepted and has beenfurther developed, but a detailed introduction is needed in orderto make the material available and accessible to a wide audience.This will be the first book providing such an introduction,covering core theory and recent developments which can be appliedto many application areas. All authors of individual chapters areleading researchers on the specific topics, assuring high qualityand up-to-date contents. An Introduction to Imprecise Probabilities provides acomprehensive introduction to imprecise probabilities, includingtheory and applications reflecting the current state if the art.Each chapter is written by experts on the respective topics,including: Sets of desirable gambles; Coherent lower (conditional)previsions; Special cases and links to literature; Decision making;Graphical models; Classification; Reliability and risk assessment;Statistical inference; Structural judgments; Aspects ofimplementation (including elicitation and computation); Models infinance; Game-theoretic probability; Stochastic processes(including Markov chains); Engineering applications. Essential reading for researchers in academia, researchinstitutes and other organizations, as well as practitionersengaged in areas such as risk analysis and engineering.

Introduction to Imprecise Probabilities

Thomas Augustin,Frank P. A. Coolen,Gert de Cooman,Matthias C. M. Troffaes
Introduction to Imprecise Probabilities Book PDF

Author : Thomas Augustin,Frank P. A. Coolen,Gert de Cooman,Matthias C. M. Troffaes
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 42,9 Mb
Release : 2014-06-03
Category : Mathematics
ISBN : 9780470973813

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Introduction to Imprecise Probabilities by Thomas Augustin,Frank P. A. Coolen,Gert de Cooman,Matthias C. M. Troffaes Pdf

In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Game-theoretic probability; Stochastic processes (including Markov chains); Engineering applications. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.

Uncertainty in Engineering

Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock
Uncertainty in Engineering Book PDF

Author : Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock
Publisher : Springer Nature
Page : 148 pages
File Size : 41,5 Mb
Release : 2022
Category : Electronic
ISBN : 9783030836405

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Uncertainty in Engineering by Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock Pdf

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.

Game-Theoretic Foundations for Probability and Finance

Glenn Shafer,Vladimir Vovk
Game Theoretic Foundations for Probability and Finance Book PDF

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 53,9 Mb
Release : 2019-03-21
Category : Business & Economics
ISBN : 9781118547939

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Game-Theoretic Foundations for Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

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

Statistical Reasoning with Imprecise Probabilities

Peter Walley
Statistical Reasoning with Imprecise Probabilities Book PDF

Author : Peter Walley
Publisher : Chapman and Hall/CRC
Page : 728 pages
File Size : 55,6 Mb
Release : 1991
Category : Mathematics
ISBN : MINN:31951D00509105X

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Statistical Reasoning with Imprecise Probabilities by Peter Walley Pdf

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

The Geometry of Uncertainty

Fabio Cuzzolin
The Geometry of Uncertainty Book PDF

Author : Fabio Cuzzolin
Publisher : Springer Nature
Page : 850 pages
File Size : 53,7 Mb
Release : 2020-12-17
Category : Computers
ISBN : 9783030631536

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The Geometry of Uncertainty by Fabio Cuzzolin Pdf

The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.

Introduction to Probability

Narayanaswamy Balakrishnan,Markos V. Koutras,Konstadinos G. Politis
Introduction to Probability Book PDF

Author : Narayanaswamy Balakrishnan,Markos V. Koutras,Konstadinos G. Politis
Publisher : John Wiley & Sons
Page : 548 pages
File Size : 46,7 Mb
Release : 2021-11-24
Category : Mathematics
ISBN : 9781118548554

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Introduction to Probability by Narayanaswamy Balakrishnan,Markos V. Koutras,Konstadinos G. Politis Pdf

INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Optimization Under Uncertainty with Applications to Aerospace Engineering

Massimiliano Vasile
Optimization Under Uncertainty with Applications to Aerospace Engineering Book PDF

Author : Massimiliano Vasile
Publisher : Springer Nature
Page : 573 pages
File Size : 43,5 Mb
Release : 2021-02-15
Category : Science
ISBN : 9783030601669

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Optimization Under Uncertainty with Applications to Aerospace Engineering by Massimiliano Vasile Pdf

In an expanding world with limited resources, optimization and uncertainty quantification have become a necessity when handling complex systems and processes. This book provides the foundational material necessary for those who wish to embark on advanced research at the limits of computability, collecting together lecture material from leading experts across the topics of optimization, uncertainty quantification and aerospace engineering. The aerospace sector in particular has stringent performance requirements on highly complex systems, for which solutions are expected to be optimal and reliable at the same time. The text covers a wide range of techniques and methods, from polynomial chaos expansions for uncertainty quantification to Bayesian and Imprecise Probability theories, and from Markov chains to surrogate models based on Gaussian processes. The book will serve as a valuable tool for practitioners, researchers and PhD students.

Probability: A Very Short Introduction

John Haigh
Probability A Very Short Introduction Book PDF

Author : John Haigh
Publisher : OUP Oxford
Page : 144 pages
File Size : 46,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780191636837

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Probability: A Very Short Introduction by John Haigh Pdf

Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all measurement, are necessarily imprecise and involve uncertainties of varying degrees, the understanding and management of probabilities is central to much work in the sciences and economics. In this Very Short Introduction, John Haigh introduces the ideas of probability and different philosophical approaches to probability, and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions, and goes on to discuss a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Probability

Robert P. Dobrow
Probability Book PDF

Author : Robert P. Dobrow
Publisher : John Wiley & Sons
Page : 366 pages
File Size : 55,8 Mb
Release : 2013-10-16
Category : Mathematics
ISBN : 9781118589441

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Probability by Robert P. Dobrow Pdf

An introduction to probability at the undergraduate level Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability. With real-life examples and thoughtful exercises from fields as diverse as biology, computer science, cryptology, ecology, public health, and sports, the book is accessible for a variety of readers. The book’s emphasis on simulation through the use of the popular R software language clarifies and illustrates key computational and theoretical results. Probability: With Applications and R helps readers develop problem-solving skills and delivers an appropriate mix of theory and application. The book includes: Chapters covering first principles, conditional probability, independent trials, random variables, discrete distributions, continuous probability, continuous distributions, conditional distribution, and limits An early introduction to random variables and Monte Carlo simulation and an emphasis on conditional probability, conditioning, and developing probabilistic intuition An R tutorial with example script files Many classic and historical problems of probability as well as nontraditional material, such as Benford’s law, power-law distributions, and Bayesian statistics A topics section with suitable material for projects and explorations, such as random walk on graphs, Markov chains, and Markov chain Monte Carlo Chapter-by-chapter summaries and hundreds of practical exercises Probability: With Applications and R is an ideal text for a beginning course in probability at the undergraduate level.

The Probability Tutoring Book

Carol Ash
The Probability Tutoring Book Book PDF

Author : Carol Ash
Publisher : Wiley-IEEE Press
Page : 0 pages
File Size : 42,7 Mb
Release : 1996-11-14
Category : Mathematics
ISBN : 0780310519

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The Probability Tutoring Book by Carol Ash Pdf

A self-study guide for practicing engineers, scientists, and students, this book offers practical, worked-out examples on continuous and discrete probability for problem-solving courses. It is filled with handy diagrams, examples, and solutions that greatly aid in the comprehension of a variety of probability problems.

Probability-Based Structural Fire Load

Leo Razdolsky
Probability Based Structural Fire Load Book PDF

Author : Leo Razdolsky
Publisher : Cambridge University Press
Page : 353 pages
File Size : 49,6 Mb
Release : 2014-08-25
Category : Mathematics
ISBN : 9781107038745

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Probability-Based Structural Fire Load by Leo Razdolsky Pdf

This book introduces the subject of probabilistic analysis to engineers and can be used as a reference in applying this technology.

Probability and Statistics with Reliability, Queuing, and Computer Science Applications

Kishor S. Trivedi
Probability and Statistics with Reliability Queuing and Computer Science Applications Book PDF

Author : Kishor S. Trivedi
Publisher : John Wiley & Sons
Page : 880 pages
File Size : 50,8 Mb
Release : 2016-06-30
Category : Computers
ISBN : 9781119314202

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Probability and Statistics with Reliability, Queuing, and Computer Science Applications by Kishor S. Trivedi Pdf

An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Introduction to Neutrosophic Statistics

Florentin Smarandache
Introduction to Neutrosophic Statistics Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 123 pages
File Size : 48,9 Mb
Release : 2014
Category : Mathematics
ISBN : 9781599732749

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Introduction to Neutrosophic Statistics by Florentin Smarandache Pdf

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate. In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of indeterminacies, depending on the problem to solve.

Rational Choice Using Imprecise Probabilities and Utilities

Paul Weirich
Rational Choice Using Imprecise Probabilities and Utilities Book PDF

Author : Paul Weirich
Publisher : Cambridge University Press
Page : 139 pages
File Size : 44,9 Mb
Release : 2021-02-25
Category : Science
ISBN : 9781108604789

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Rational Choice Using Imprecise Probabilities and Utilities by Paul Weirich Pdf

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement.