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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
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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: Donald Gillies
Publisher: Routledge
ISBN: 1134672454
Category : Philosophy
Languages : en
Pages : 239
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Book Description
The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.
Author: Bruno De Finetti
Publisher: John Wiley & Sons
ISBN: 9780471588825
Category : Probabilities
Languages : en
Pages : 0
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Book Description
Author: Richard von Mises
Publisher: Academic Press
ISBN: 1483264025
Category : Mathematics
Languages : en
Pages : 709
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Book Description
Mathematical Theory of Probability and Statistics focuses on the contributions and influence of Richard von Mises on the processes, methodologies, and approaches involved in the mathematical theory of probability and statistics. The publication first elaborates on fundamentals, general label space, and basic properties of distributions. Discussions focus on Gaussian distribution, Poisson distribution, mean value variance and other moments, non-countable label space, basic assumptions, operations, and distribution function. The text then ponders on examples of combined operations and summation of chance variables characteristic function. The book takes a look at the asymptotic distribution of the sum of chance variables and probability inference. Topics include inference from a finite number of observations, law of large numbers, asymptotic distributions, limit distribution of the sum of independent discrete random variables, probability of the sum of rare events, and probability density. The text also focuses on the introduction to the theory of statistical functions and multivariate statistics. The publication is a dependable source of information for researchers interested in the mathematical theory of probability and statistics
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Category : Mathematics
Languages : en
Pages :
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Book Description
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Author: Roy Weatherford
Publisher: Taylor & Francis
ISBN: 1000626091
Category : Philosophy
Languages : en
Pages : 220
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Book Description
First published in 1982, Philosophical Foundations of Probability Theory starts with the uses we make of the concept in everyday life and then examines the rival theories that seek to account for these applications. It offers a critical exposition of the major philosophical theories of probability, with special attention given to the metaphysical and epistemological assumptions and implications of each. The Classical Theory suggests probability is simply the ratio of favorable cases to all equi-possible cases: it is this theory that is relied on by gamblers and by most non-specialists. The A Priori Theory, on the other hand, describes probability as a logical relation between statements based on evidence. The Relative Frequency theories locate it not in logic but among empirical rates of occurrence in the real world, while the Subjectivist Theory identifies probability with the degree of a person’s belief in a proposition. Each of these types of theory is examined in turn, and the treatment is unified by the use of running examples and parallel analyses of each theory. The final chapter includes a summary and the author’s conclusions. This book is an essential read for scholars and researchers of Philosophy.
Author: W.L. Harper
Publisher: Springer Science & Business Media
ISBN: 9789027706171
Category : Gardening
Languages : en
Pages : 334
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Book Description
Proceedings of an International Research Colloquium held at the University of Western Ontario, 10-13 May 1973.
Author: J. L. Doob
Publisher: Springer Science & Business Media
ISBN: 1461252083
Category : Mathematics
Languages : en
Pages : 865
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Book Description
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
Author: Richard Von Mises
Publisher: Courier Corporation
ISBN: 0486242145
Category : Mathematics
Languages : en
Pages : 273
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Book Description
This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.
Author:
Publisher: Allied Publishers
ISBN: 9788177644517
Category :
Languages : en
Pages : 436
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Book Description
Probability theory
