Book•
A mathematical theory of evidence
01 Jan 1976-
TL;DR: This book develops 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.
Abstract: 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.
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01 Jan 1988TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Abstract: From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
15,671 citations
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
8,918 citations
TL;DR: In this paper, a survey of spectrum sensing methodologies for cognitive radio is presented and the cooperative sensing concept and its various forms are explained.
Abstract: The spectrum sensing problem has gained new aspects with cognitive radio and opportunistic spectrum access concepts. It is one of the most challenging issues in cognitive radio systems. In this paper, a survey of spectrum sensing methodologies for cognitive radio is presented. Various aspects of spectrum sensing problem are studied from a cognitive radio perspective and multi-dimensional spectrum sensing concept is introduced. Challenges associated with spectrum sensing are given and enabling spectrum sensing methods are reviewed. The paper explains the cooperative sensing concept and its various forms. External sensing algorithms and other alternative sensing methods are discussed. Furthermore, statistical modeling of network traffic and utilization of these models for prediction of primary user behavior is studied. Finally, sensing features of some current wireless standards are given.
4,812 citations
Book•
01 Jul 2002TL;DR: In this article, a review is presented of the book "Heuristics and Biases: The Psychology of Intuitive Judgment, edited by Thomas Gilovich, Dale Griffin, and Daniel Kahneman".
Abstract: A review is presented of the book “Heuristics and Biases: The Psychology of Intuitive Judgment,” edited by Thomas Gilovich, Dale Griffin, and Daniel Kahneman.
3,642 citations
References
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01 Jun 1960
TL;DR: Theories of ProbabilityFoundation of Probabilistic Logic ProgrammingGood ThinkingStatistical Foundations of Data ScienceFoundations of Risk Analysis foundations of Estimation Theory findations of the theory of probability.
Abstract: Theories of ProbabilityFoundations of Probabilistic Logic ProgrammingGood ThinkingStatistical Foundations of Data ScienceFoundations of Risk AnalysisFoundations of Estimation TheoryThe Foundations of StatisticsProbability Theory in FinanceFoundations of Agnostic StatisticsProbability, Statistics, and TruthFoundations of ProbabilityFoundations of Quantization for Probability DistributionsMathematical Foundations of the Calculus of ProbabilityThe Foundations of Causal Decision TheoryAn Objective Theory of Probability (Routledge Revivals)Probability TheoryDelaware Seminar in the Foundations of PhysicsFoundations of Stochastic AnalysisTheoretical Foundations of Functional Data Analysis, with an Introduction to Linear OperatorsTheories of ProbabilityProbabilistic Foundations of Statistical Network AnalysisElements of the Theory of Functions and Functional Analysis [Two Volumes in One]Probability TheoryPhilosophical Foundations of Probability TheoryProbability Foundations of Economic TheoryGame-Theoretic Foundations for Probability and FinanceFoundations of Statistical MechanicsProbability Foundations for EngineersFoundations of Data ScienceFoundations and Philosophy of Epistemic Applications of Probability TheoryFoundations of Probability Theory, Statistical Inference, and Statistical Theories of ScienceRandom Measures, Theory and ApplicationsModern Probability Theory and Its ApplicationsRethinking the Foundations of StatisticsMathematical Foundations of Information TheoryFoundations of the Theory of ProbabilityFoundations of Modern ProbabilityFoundations of the theory of probabilityMathematical Foundations of Infinite-Dimensional Statistical ModelsFoundations of Statistics
1,822 citations
"A mathematical theory of evidence" refers background in this paper
...noted by Kolmogorov [6] when he said " ....
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...While it has been explicated mathematically, via the probability of a joint event formed from independent events being equal to the product of their individual probabilities, the adequacy of this explication of our intuitive concept has been questioned [5], and the importance of this issue has been noted by Kolmogorov [6] when he said " . . . one of the most important problems in the philosophy of the natural sciences is . . . to make precise the premises which would make it possible to regard any given real events as independent."...
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