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Author: Richard T. Cox
Publisher: Johns Hopkins University Press
ISBN: 9780801869822
Category : Mathematics
Languages : en
Pages : 0
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Book Description
In Algebra of Probable Inference, Richard T. Cox develops and demonstrates that probability theory is the only theory of inductive inference that abides by logical consistency. Cox does so through a functional derivation of probability theory as the unique extension of Boolean Algebra thereby establishing, for the first time, the legitimacy of probability theory as formalized by Laplace in the 18th century. Perhaps the most significant consequence of Cox's work is that probability represents a subjective degree of plausible belief relative to a particular system but is a theory that applies universally and objectively across any system making inferences based on an incomplete state of knowledge. Cox goes well beyond this amazing conceptual advancement, however, and begins to formulate a theory of logical questions through his consideration of systems of assertions—a theory that he more fully developed some years later. Although Cox's contributions to probability are acknowledged and have recently gained worldwide recognition, the significance of his work regarding logical questions is virtually unknown. The contributions of Richard Cox to logic and inductive reasoning may eventually be seen to be the most significant since Aristotle.
Author: Richard T. Cox
Publisher: Johns Hopkins University Press
ISBN: 9780801869822
Category : Mathematics
Languages : en
Pages : 0
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Book Description
In Algebra of Probable Inference, Richard T. Cox develops and demonstrates that probability theory is the only theory of inductive inference that abides by logical consistency. Cox does so through a functional derivation of probability theory as the unique extension of Boolean Algebra thereby establishing, for the first time, the legitimacy of probability theory as formalized by Laplace in the 18th century. Perhaps the most significant consequence of Cox's work is that probability represents a subjective degree of plausible belief relative to a particular system but is a theory that applies universally and objectively across any system making inferences based on an incomplete state of knowledge. Cox goes well beyond this amazing conceptual advancement, however, and begins to formulate a theory of logical questions through his consideration of systems of assertions—a theory that he more fully developed some years later. Although Cox's contributions to probability are acknowledged and have recently gained worldwide recognition, the significance of his work regarding logical questions is virtually unknown. The contributions of Richard Cox to logic and inductive reasoning may eventually be seen to be the most significant since Aristotle.
Author: Richard T. Cox
Publisher:
ISBN:
Category : Algebra, Boolean
Languages : en
Pages : 114
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Book Description
Author: Richard Threlkeld Cox
Publisher:
ISBN:
Category : Algebra, Boolean
Languages : en
Pages : 114
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Book Description
Author: W.T. Grandy Jr.
Publisher: Springer Science & Business Media
ISBN: 9400938675
Category : Science
Languages : en
Pages : 391
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Book Description
In a certain sense this book has been twenty-five years in the writing, since I first struggled with the foundations of the subject as a graduate student. It has taken that long to develop a deep appreciation of what Gibbs was attempting to convey to us near the end of his life and to understand fully the same ideas as resurrected by E.T. Jaynes much later. Many classes of students were destined to help me sharpen these thoughts before I finally felt confident that, for me at least, the foundations of the subject had been clarified sufficiently. More than anything, this work strives to address the following questions: What is statistical mechanics? Why is this approach so extraordinarily effective in describing bulk matter in terms of its constituents? The response given here is in the form of a very definite point of view-the principle of maximum entropy (PME). There have been earlier attempts to approach the subject in this way, to be sure, reflected in the books by Tribus [Thermostat ics and Thermodynamics, Van Nostrand, 1961], Baierlein [Atoms and Information Theory, Freeman, 1971], and Hobson [Concepts in Statistical Mechanics, Gordon and Breach, 1971].
Author: Augustus De Morgan
Publisher:
ISBN:
Category : Logic
Languages : en
Pages : 376
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Book Description
Author: David. H Wolpert
Publisher: CRC Press
ISBN: 0429961073
Category : Mathematics
Languages : en
Pages : 460
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Book Description
This book provides different mathematical frameworks for addressing supervised learning. It is based on a workshop held under the auspices of the Center for Nonlinear Studies at Los Alamos and the Santa Fe Institute in the summer of 1992.
Author: Sylvia Weiser
Publisher:
ISBN:
Category : Engineering
Languages : en
Pages : 234
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Book Description
Author: Gudwin, Ricardo
Publisher: IGI Global
ISBN: 1599040654
Category : Computers
Languages : en
Pages : 368
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Book Description
"This book assembles semiotics and artificial intelligence techniques in order to design new kinds of intelligence systems; it changes the research field of artificial intelligence by incorporating the study of meaning processes (semiosis), from the perspective of formal sciences, linguistics, and philosophy"--Provided by publisher.
Author: Phil Gregory
Publisher: Cambridge University Press
ISBN: 113944428X
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.
Author: Mehdi Khosrow-Pour
Publisher: IGI Global Snippet
ISBN: 9781605660264
Category : Computers
Languages : en
Pages : 4292
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Book Description
"This set of books represents a detailed compendium of authoritative, research-based entries that define the contemporary state of knowledge on technology"--Provided by publisher.
