Mathematical Theory of Evidence (eBook)

Glenn Shafer (Autor)

eBook Download: PDF

2020
314 Seiten
Princeton University Press (Verlag)
978-0-691-21469-6 (ISBN)

Infos

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 "e;lower probabilities"e; as epistemic probabilities and taking his rule for combining "e;upper and lower probabilities"e; 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 "e;monotone of order of infinity."e; and Dempster's rule for combining such set functions. This rule, together with the idea of "e;weights of evidence,"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 7.7.2020
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Schlagworte: Accuracy and precision • A priori probability • Argument of a function • assessment of evidence • Bayesian • Bayesian belief functions • Bayesian inference • Bayesian probability • Bayesian Statistics • Bayes' Theorem • Binomial Theorem • Calculation • Cartesian Product • Categorical Proposition • Causality • chance density • combination • Confidence interval • confidence sets • Decision Theory • degree of belief • Dempster–Shafer Theory • Determinism • Dissonance • Epistemology • Equation • estimation • Estimation theory • existential quantification • Explanation • exponential function • Foundations of statistics • Frequentist probability • Function (mathematics) • general knowledge • Geometry • Granger, Thomas • Hacking, Ian • hypothesis • idealization • inductive reasoning • inference • Infimum and supremum • Instance (computer science) • Intersection (set theory) • Jeffrey, Richard • judgment and evidence • Keynes, John Maynard • Law of thought • likelihood • Likelihood Function • Limiting case (mathematics) • Limit (mathematics) • Limit of a sequence • linear model • linear models • Linear space (geometry) • logarithm • Logic • Logical conjunction • logical consequence • Logical disjunction • Mathematical Analysis • Mathematical Notation • Mathematical problem • Mathematical Statistics • mathematical structure • Mathematical Theory • mathematician • Mathematics • Modern Physics • natural logarithm • Naturalness (physics) • Negation • Notation • Numerical analysis • orthogonal sum • pairwise • Parameter (computer programming) • parametric model • Parity (mathematics) • Philosophy • Plausibility • Practical reason • premise • Principle of rationality • Prior probability • Probability • Probability Theory • Proportionality (mathematics) • Proposition • Quantity • quantum mechanics • quasi support function • reason • Restriction (mathematics) • Richard Jeffrey • school of thought • scientific evidence • scientific hypotheses • scientific notation • scientific theory • Scientist • Set notation • Sign (mathematics) • Special case • Statistical estimation • Statistical hypothesis testing • Statistical Inference • statistical significance • Statistics • Subset • Summation • Support function • test statistic • The Doctrine of Chances • Theorem • theory • The Philosopher • Unification (computer science) • Units of measurement • upper probability
• ISBN-10: 0-691-21469-7 / 0691214697
• ISBN-13: 978-0-691-21469-6 / 9780691214696