Statistical Reasoning With Imprecise Probabilities
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Statistical Reasoning With Imprecise Probabilities
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Author : Peter Walley
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1991
Statistical Reasoning With Imprecise Probabilities written by Peter Walley and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
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.
Statistical Reasoning With Imprecise Probabilities
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Author : Peter Walley
language : en
Publisher: Springer
Release Date :
Statistical Reasoning With Imprecise Probabilities written by Peter Walley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
When I started writing this book, my mind was full of ignorance and uncertainty, particularly about how best to deal with ignorance and uncertainty. Much of the ignorance and uncertainty remains, now that the book is finished, but it is organized more coherently. I see that as progress. As the title indicates, the book is about methods of reasoning and statistical inference using imprecise probabilities. The methods are based on a behavioural interpretation of probability and principles of coherence. The idea for such a book originated in 1982, after I had written two long reports on the mathematics and elicitation of upper and lower probabilities. My experience in teaching and applying the existing theories of statistical inference had convinced me that each of them was inadequate. The Bayesian theory is inadequate, despite its great virtues of coherence, because it requires all probability assessments to be precise yet gives little guidance on how to make them. It seemed natural to investigate whether the Bayesian theory could be modified by admitting imprecise probabilities as models for partial ignorance. Is it possible to reconcile imprecision with coherence, vagueness with rationality? Fortunately the ans wer is yes! The basic ideas of the book appeared in the two technical reports (1981, 1982). The coherence principles for conditional probabilities and statistical models were worked out in New Zealand, in 1983.
Introduction To Imprecise Probabilities
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Author : Thomas Augustin
language : en
Publisher: John Wiley & Sons
Release Date : 2014-06-03
Introduction To Imprecise Probabilities written by Thomas Augustin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-03 with Mathematics categories.
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
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Author : Louis J. M. Aslett
language : en
Publisher: Springer Nature
Release Date : 2021-12-09
Uncertainty In Engineering written by Louis J. M. Aslett and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-09 with Mathematics categories.
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.
Medical Pharmacology
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Author : Peter Winstanley
language : en
Publisher: Elsevier Health Sciences
Release Date : 2007-01-01
Medical Pharmacology written by Peter Winstanley and has been published by Elsevier Health Sciences this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Medical categories.
Approached from the point of view of what you will need to know in order to understand the clinical work you will eventually be doing, this title includes a wide range of self-assessment material, suitable for testing your understanding, and helping you to prepare for your exams.
The Geometry Of Uncertainty
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Author : Fabio Cuzzolin
language : en
Publisher: Springer Nature
Release Date : 2020-12-17
The Geometry Of Uncertainty written by Fabio Cuzzolin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Computers categories.
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.
The Engineering Statistician S Guide To Continuous Bivariate Distributions
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Author : T. P. Hutchinson
language : en
Publisher:
Release Date : 1991
The Engineering Statistician S Guide To Continuous Bivariate Distributions written by T. P. Hutchinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Quantified Representation Of Uncertainty And Imprecision
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Quantified Representation Of Uncertainty And Imprecision written by Dov M. Gabbay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Philosophy categories.
We are happy to present the first volume of the Handbook of Defeasible Reasoning and Uncertainty Management Systems. Uncertainty pervades the real world and must therefore be addressed by every system that attempts to represent reality. The representation of uncertainty is a ma jor concern of philosophers, logicians, artificial intelligence researchers and com puter sciencists, psychologists, statisticians, economists and engineers. The present Handbook volumes provide frontline coverage of this area. This Handbook was produced in the style of previous handbook series like the Handbook of Philosoph ical Logic, the Handbook of Logic in Computer Science, the Handbook of Logic in Artificial Intelligence and Logic Programming, and can be seen as a companion to them in covering the wide applications of logic and reasoning. We hope it will answer the needs for adequate representations of uncertainty. This Handbook series grew out of the ESPRIT Basic Research Project DRUMS II, where the acronym is made out of the Handbook series title. This project was financially supported by the European Union and regroups 20 major European research teams working in the general domain of uncertainty. As a fringe benefit of the DRUMS project, the research community was able to create this Hand book series, relying on the DRUMS participants as the core of the authors for the Handbook together with external international experts.
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Author :
language : en
Publisher: IOS Press
Release Date :
written by and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Soft Methods In Probability Statistics And Data Analysis
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Author : Przemyslaw Grzegorzewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Soft Methods In Probability Statistics And Data Analysis written by Przemyslaw Grzegorzewski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.