Mathematical Theory of Evidence
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A priori probability
A01=Glenn Shafer
Accuracy and precision
Argument of a function
Author_Glenn Shafer
Bayes' theorem
Bayesian
Bayesian inference
Bayesian probability
Bayesian statistics
Calculation
Categorical proposition
Category=PBX
Dempster-Shafer theory
Determinism
Epistemology
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Estimation
Estimation theory
Existential quantification
Explanation
Foundations of statistics
Frequentist probability
Function (mathematics)
Geometry
Hypothesis
Idealization
Inductive reasoning
Inference
Instance (computer science)
Intersection (set theory)
Limit (mathematics)
Limit of a sequence
Limiting case (mathematics)
Logarithm
Logic
Logical conjunction
Logical disjunction
Mathematical analysis
Mathematical notation
Mathematical problem
Mathematical statistics
Mathematical structure
Mathematical theory
Mathematician
Mathematics
Modern physics
Naturalness (physics)
Numerical analysis
Parametric model
Parity (mathematics)
Probability
Probability theory
Proportionality (mathematics)
Quantity
Reason
Restriction (mathematics)
Scientific evidence
Scientific notation
Scientific theory
Sign (mathematics)
Special case
Statistical hypothesis testing
Statistical inference
Statistical significance
Subset
Summation
Support function
Test statistic
The Philosopher
Theorem
Theory
Unification (computer science)
Product details
- ISBN 9780691100425
- Weight: 425g
- Dimensions: 152 x 235mm
- Publication Date: 21 Apr 1976
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Glenn Shafer is professor at Rutgers University and director of the Ph.D. program.
