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Author: Terrence L. Fine
Publisher: Academic Press
ISBN: 1483263894
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.
Author: Terrence L. Fine
Publisher: Academic Press
ISBN: 1483263894
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.
Author: Rudolf Carnap
Publisher: Univ of California Press
ISBN: 0520334256
Category : Mathematics
Languages : en
Pages : 270
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Book Description
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.
Author: Daniel Courgeau
Publisher: Springer Science & Business Media
ISBN: 9400728794
Category : Social Science
Languages : en
Pages : 333
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Book Description
This work examines in depth the methodological relationships that probability and statistics have maintained with the social sciences from their emergence. It covers both the history of thought and current methods. First it examines in detail the history of the different paradigms and axioms for probability, from their emergence in the seventeenth century up to the most recent developments of the three major concepts: objective, subjective and logicist probability. It shows the statistical inference they permit, different applications to social sciences and the main problems they encounter. On the other side, from social sciences—particularly population sciences—to probability, it shows the different uses they made of probabilistic concepts during their history, from the seventeenth century, according to their paradigms: cross-sectional, longitudinal, hierarchical, contextual and multilevel approaches. While the ties may have seemed loose at times, they have more often been very close: some advances in probability were driven by the search for answers to questions raised by the social sciences; conversely, the latter have made progress thanks to advances in probability. This dual approach sheds new light on the historical development of the social sciences and probability, and on the enduring relevance of their links. It permits also to solve a number of methodological problems encountered all along their history.
Author: W.L. Harper
Publisher: Springer Science & Business Media
ISBN: 9401014361
Category : Science
Languages : en
Pages : 464
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Book Description
In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory. The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Bayesian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference. Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.
Author: M. Swain
Publisher: Springer Science & Business Media
ISBN: 9401033900
Category : Science
Languages : en
Pages : 241
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Book Description
The papers collected in this volume were originally presented at a sym posium held at the University of Pennsylvania in December of 1968. Each of the papers has been revised in light of the discussions that took place during this symposium. None of the papers has appeared in print previously. The extensive bibliography that appears at the end of the volume was originally distributed during the symposium and was revised on the basis of many helpful suggestions made by those who participated. The symposium was made possible by a grant from The National Science Foundation and funds contributed by the Philosophy Depart ment of the University of Pennsylvania. On behalf of the contributors to this volume, I would like to express my thanks to these organizations for their generous support. In addition, I would like to express my gratitude to the members of the Graduate Philosophy Students Organization at the University of Penn sylvania for the considerable assistance they gave me during the sym posium. My thanks, also, to Judith Sofranko and Lynn Luckett for their very responsible efforts in the preparation of the manuscript. Finally, I would like to thank Professor James Cornman for his invaluable advice and encouragement.
Author: Joseph B. Kadane
Publisher: Cambridge University Press
ISBN: 9780521649759
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists.
Author: Leonard J. Savage
Publisher: Courier Corporation
ISBN: 0486137104
Category : Mathematics
Languages : en
Pages : 341
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Book Description
Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.
Author: Halina Mortimer
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 192
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Book Description
Author: Wesley C. Salmon
Publisher: University of Pittsburgh Press
ISBN: 0822982943
Category : Science
Languages : en
Pages : 298
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Book Description
After its publication in 1967, The Foundations of Scientific Inference taught a generation of students and researchers about the problem of induction, the interpretation of probability, and confirmation theory. Fifty years later, Wesley C. Salmon’s book remains one of the clearest introductions to these fundamental problems in the philosophy of science. This anniversary edition of Salmon’s foundational work features a detailed introduction by Christopher Hitchcock, which examines the book’s origins, influences, and major themes, its impact and enduring effects, the disputes it raised, and its place in current studies, revisiting Salmon’s ideas for a new audience of philosophers, historians, scientists, and students.
Author: Henry Ely Kyburg
Publisher: Cambridge University Press
ISBN: 9780521001014
Category : Computers
Languages : en
Pages : 318
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Book Description
This book presents a clear exposition of the approaches to the problem of uncertain inference.
