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Author : Paul-Andre Monney
Publisher : Springer
ISBN 13 : 9783642517471
Total Pages : 174 pages
Book Rating : 4.5/5 (174 download)
Download or read book A Mathematical Theory of Arguments for Statistical Evidence written by Paul-Andre Monney and published by Springer. This book was released on 2014-01-15 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul-Andre Monney
Publisher : Springer Science & Business Media
ISBN 13 : 3642517463
Total Pages : 160 pages
Book Rating : 4.6/5 (425 download)
Download or read book A Mathematical Theory of Arguments for Statistical Evidence written by Paul-Andre Monney and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the reasoning under uncertainty based on sta tistical evidence, where the word reasoning is taken to mean searching for arguments in favor or against particular hypotheses of interest. The kind of reasoning we are using is composed of two aspects. The first one is inspired from classical reasoning in formal logic, where deductions are made from a knowledge base of observed facts and formulas representing the domain spe cific knowledge. In this book, the facts are the statistical observations and the general knowledge is represented by an instance of a special kind of sta tistical models called functional models. The second aspect deals with the uncertainty under which the formal reasoning takes place. For this aspect, the theory of hints [27] is the appropriate tool. Basically, we assume that some uncertain perturbation takes a specific value and then logically eval uate the consequences of this assumption. The original uncertainty about the perturbation is then transferred to the consequences of the assumption. This kind of reasoning is called assumption-based reasoning. Before going into more details about the content of this book, it might be interesting to look briefly at the roots and origins of assumption-based reasoning in the statistical context. In 1930, R. A. Fisher [17] defined the notion of fiducial distribution as the result of a new form of argument, as opposed to the result of the older Bayesian argument.
Author : Glenn Shafer
Publisher :
ISBN 13 : 9780608025087
Total Pages : 302 pages
Book Rating : 4.0/5 (25 download)
Download or read book A Mathematical Theory of Evidence written by Glenn Shafer and published by . This book was released on 1976 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giovanni Sommaruga
Publisher : Springer
ISBN 13 : 3642006590
Total Pages : 275 pages
Book Rating : 4.6/5 (42 download)
Download or read book Formal Theories of Information written by Giovanni Sommaruga and published by Springer. This book was released on 2009-04-07 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is commonly assumed that computers process information. But what is inf- mation? In a technical, important, but nevertheless rather narrow sense, Sh- non’sinformationtheorygivesa?rstanswertothisquestion.Thistheoryfocuses on measuring the information content of a message. Essentially this measure is the reduction of the uncertainty obtained by receiving a message. The unc- tainty of a situation of ignorance in turn is measured by entropy. This theory hashad an immense impact on the technologyof information storage,data c- pression, information transmission and coding and still is a very active domain of research. Shannon’s theory has also attractedmuch interest in a more philosophic look at information, although it was readily remarked that it is only a “syntactic” theory of information and neglects “semantic” issues. Several attempts have been made in philosophy to give information theory a semantic ?avor, but still mostly based on or at least linked to Shannon’s theory. Approaches to semantic informationtheoryalsoveryoftenmakeuseofformallogic.Thereby,information is linked to reasoning, deduction and inference, as well as to decision making. Further, entropy and related measure were soon found to have important connotations with regard to statistical inference. Surely, statistical data and observation represent information, information about unknown, hidden para- ters. Thus a whole branch of statistics developed around concepts of Shannon’s information theory or derived from them. Also some proper measurements - propriate for statistics, like Fisher’s information, were proposed.
Author : Juerg Kohlas
Publisher : Springer Science & Business Media
ISBN 13 : 3662016745
Total Pages : 430 pages
Book Rating : 4.6/5 (62 download)
Download or read book A Mathematical Theory of Hints written by Juerg Kohlas and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: An approach to the modeling of and the reasoning under uncertainty. The book develops the Dempster-Shafer Theory with regard to the reliability of reasoning with uncertain arguments. Of particular interest here is the development of a new synthesis and the integration of logic and probability theory. The reader benefits from a new approach to uncertainty modeling which extends classical probability theory.
Author : Glenn Shafer
Publisher : Princeton University Press
ISBN 13 : 0691214697
Total Pages : pages
Book Rating : 4.6/5 (912 download)
Download or read book A Mathematical Theory of Evidence written by Glenn Shafer and published by Princeton University Press. This book was released on 2020-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.
Author : Weiru Liu
Publisher : Springer Science & Business Media
ISBN 13 : 3642221513
Total Pages : 775 pages
Book Rating : 4.6/5 (422 download)
Download or read book Symbolic and Quantitative Approaches to Reasoning with Uncertainty written by Weiru Liu and published by Springer Science & Business Media. This book was released on 2011-06-24 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2011, held in Belfast, UK, in June/July 2011. The 60 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 108 submissions. The papers are organized in topical sections on argumentation; Bayesian networks and causal networks; belief functions; belief revision and inconsistency handling; classification and clustering; default reasoning and logics for reasoning under uncertainty; foundations of reasoning and decision making under uncertainty; fuzzy sets and fuzzy logic; implementation and applications of uncertain systems; possibility theory and possibilistic logic; and uncertainty in databases.
Author : Robert P. Abelson
Publisher : Psychology Press
ISBN 13 : 1135694419
Total Pages : 242 pages
Book Rating : 4.1/5 (356 download)
Download or read book Statistics As Principled Argument written by Robert P. Abelson and published by Psychology Press. This book was released on 2012-09-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this illuminating volume, Robert P. Abelson delves into the too-often dismissed problems of interpreting quantitative data and then presenting them in the context of a coherent story about one's research. Unlike too many books on statistics, this is a remarkably engaging read, filled with fascinating real-life (and real-research) examples rather than with recipes for analysis. It will be of true interest and lasting value to beginning graduate students and seasoned researchers alike. The focus of the book is that the purpose of statistics is to organize a useful argument from quantitative evidence, using a form of principled rhetoric. Five criteria, described by the acronym MAGIC (magnitude, articulation, generality, interestingness, and credibility) are proposed as crucial features of a persuasive, principled argument. Particular statistical methods are discussed, with minimum use of formulas and heavy data sets. The ideas throughout the book revolve around elementary probability theory, t tests, and simple issues of research design. It is therefore assumed that the reader has already had some access to elementary statistics. Many examples are included to explain the connection of statistics to substantive claims about real phenomena.
Author : Fabio Cuzzolin
Publisher : Springer Nature
ISBN 13 : 3030631532
Total Pages : 850 pages
Book Rating : 4.0/5 (36 download)
Download or read book The Geometry of Uncertainty written by Fabio Cuzzolin and published by Springer Nature. This book was released on 2020-12-17 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Yoel Haitovsky
Publisher : Springer Science & Business Media
ISBN 13 : 3642574106
Total Pages : 227 pages
Book Rating : 4.6/5 (425 download)
Download or read book Foundations of Statistical Inference written by Yoel Haitovsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers presented at a conference held in Shoresh Holiday Resort near Jerusalem, Israel, in December 2000 organized by the Israeli Ministry of Science, Culture and Sport. The theme of the conference was "Foundation of Statistical Inference: Applications in the Medical and Social Sciences and in Industry and the Interface of Computer Sciences". The following is a quotation from the Program and Abstract booklet of the conference. "Over the past several decades, the field of statistics has seen tremendous growth and development in theory and methodology. At the same time, the advent of computers has facilitated the use of modern statistics in all branches of science, making statistics even more interdisciplinary than in the past; statistics, thus, has become strongly rooted in all empirical research in the medical, social, and engineering sciences. The abundance of computer programs and the variety of methods available to users brought to light the critical issues of choosing models and, given a data set, the methods most suitable for its analysis. Mathematical statisticians have devoted a great deal of effort to studying the appropriateness of models for various types of data, and defining the conditions under which a particular method work. " In 1985 an international conference with a similar title* was held in Is rael. It provided a platform for a formal debate between the two main schools of thought in Statistics, the Bayesian, and the Frequentists.
Author : Didier Dubois
Publisher : Springer Science & Business Media
ISBN 13 : 3540850279
Total Pages : 436 pages
Book Rating : 4.5/5 (48 download)
Download or read book Soft Methods for Handling Variability and Imprecision written by Didier Dubois and published by Springer Science & Business Media. This book was released on 2008-10-01 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.
Author : Robert P. Abelson
Publisher : Psychology Press
ISBN 13 : 0805805273
Total Pages : 242 pages
Book Rating : 4.8/5 (58 download)
Download or read book Statistics as Principled Argument written by Robert P. Abelson and published by Psychology Press. This book was released on 1995 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this illuminating volume, Robert P. Abelson delves into the too-often dismissed problems of interpreting quantitative data and then presenting them in the context of a coherent story about one's research. Unlike too many books on statistics, this is a remarkably engaging read, filled with fascinating real-life (and real-research) examples rather than with recipes for analysis. It will be of true interest and lasting value to beginning graduate students and seasoned researchers alike. The focus of the book is that the purpose of statistics is to organize a useful argument from quantitative evidence, using a form of principled rhetoric. Five criteria, described by the acronym MAGIC (magnitude, articulation, generality, interestingness, and credibility) are proposed as crucial features of a persuasive, principled argument. Particular statistical methods are discussed, with minimum use of formulas and heavy data sets. The ideas throughout the book revolve around elementary probability theory, t tests, and simple issues of research design. It is therefore assumed that the reader has already had some access to elementary statistics. Many examples are included to explain the connection of statistics to substantive claims about real phenomena.
Author : Jesus Lopez-Fidalgo
Publisher : Springer Science & Business Media
ISBN 13 : 3790819522
Total Pages : 241 pages
Book Rating : 4.7/5 (98 download)
Download or read book mODa 8 - Advances in Model-Oriented Design and Analysis written by Jesus Lopez-Fidalgo and published by Springer Science & Business Media. This book was released on 2007-05-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 8th Workshop on Model-Oriented Design and Analysis. It offers leading and pioneering work on optimal experimental designs, both from a mathematical/statistical point of view and with regard to real applications. Scientists from all over the world have contributed to this volume. Primary topics are designs for nonlinear models and applications to experimental medicine.
Author : Alessandro Di Bucchianico
Publisher : Springer Science & Business Media
ISBN 13 : 3790826936
Total Pages : 239 pages
Book Rating : 4.7/5 (98 download)
Download or read book MODA 7 - Advances in Model-Oriented Design and Analysis written by Alessandro Di Bucchianico and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the proceedings of the 7th Workshop on Model-Oriented Design and Analysis which has had the purpose of bringing together leading researchers in Eastern and Western Europe for an in-depth discussion of the optimal design of experiments. The papers are representative of the latest developments concerning non-linear models, computational algorithms and important applications, especially to medical statistics.
Author : Stefan Sperlich
Publisher : Springer Science & Business Media
ISBN 13 : 3790817015
Total Pages : 185 pages
Book Rating : 4.7/5 (98 download)
Download or read book The Art of Semiparametrics written by Stefan Sperlich and published by Springer Science & Business Media. This book was released on 2006-07-25 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of articles emerged from different works presented "The Art of Semiparametrics" conference in 2003 in Berlin. It offers a collection of individual works that together show the large spectrum of semiparametric statistics. The book combines theoretical contributions with more applied and empirical studies. Although each article represents an original contribution to its own field, all are written in a self-contained way that may be read by non-experts.
Author : Camilo Dagum
Publisher : Springer Science & Business Media
ISBN 13 : 3790826812
Total Pages : 307 pages
Book Rating : 4.7/5 (98 download)
Download or read book Household Behaviour, Equivalence Scales, Welfare and Poverty written by Camilo Dagum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: A group of scholars converging on a common and socially relevant economic theme of research, that of households' welfare and poverty, met several times in the last two years to discuss the research progress and the opportunity to bring to gether for publication the research so far accomplished. They shared a research project supported by a grant from the former Italian Ministero dell'Universita e della Ricerca Scientifica e Tecnologica (MURST) now Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR): The Equiva lence Scales in the Measurement of Households' Welfare: Statistical, Economic and Demographic Analysis. The decisive meeting, an international seminar on the topics, was hosted by the University of Florence, siege of the national coordinator of this project. When one think of Florence, it is inevitable to think of the unfolding of Ren aissance, and reciprocally. th To the eyes of a traveller who had arrived to Florence in the 15 century, the city would have appeared as a sort of El Dorado, similarly to what would have occurred to the first conquerors of the South America's lands, so much astonishing were the richness of arts and the opulence of life. The flourishing of painting and sculpture had not equal all over the world and was reaching tops never made equal before. Masaccio, Brunelleschi, Donatello and later on Leonardo and Michelangelo, were the artistic and intellectual genius that enlightened beauty lovers princes.....
Author : Mark Kac
Publisher : American Mathematical Soc.
ISBN 13 : 0883850257
Total Pages : 94 pages
Book Rating : 4.8/5 (838 download)
Download or read book Statistical Independence in Probability, Analysis, and Number Theory written by Mark Kac and published by American Mathematical Soc.. This book was released on 1959-12-31 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Kac's monograph is designed to illustrate how simple observations can be made the starting point of rich and fruitful theories and how the same theme recurs in seemingly unrelated disciplines. An elementary but thorough discussion of the game of "heads or tails," including the normal law and the laws of large numbers, is presented in a setting in which a variety of purely analytic results appear natural and inevitable. The chapter "Primes Play a Game of Chance" uses the same setting in dealing with problems of the distribution of values of arithmetic functions. The final chapter "From Kinetic Theory to Continued Fractions" deals with a spectacular application of the ergodic theorems to continued fractions. Mark Kac conveyed his infectious enthusiasm for mathematics and its applications in his lectures, papers, and books. Two of his papers won Chauvenet awards for expository excellence.
