A Mathematical Theory of Evidence:
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 diverg...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2021]
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| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-859 DE-860 DE-863 DE-862 DE-739 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Mrz 2021) |
| Beschreibung: | 1 online resource (314 pages) |
| ISBN: | 9780691214696 |
| DOI: | 10.1515/9780691214696 |
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| 520 | |a 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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| index_date | 2024-07-03T17:14:52Z |
| indexdate | 2025-02-20T07:02:05Z |
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| isbn | 9780691214696 |
| language | English |
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| publisher | Princeton University Press |
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| spellingShingle | Shafer, Glenn 1946- A Mathematical Theory of Evidence MATHEMATICS / History & Philosophy bisacsh Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie (DE-588)4395834-5 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4395834-5 (DE-588)4137007-7 (DE-588)4064324-4 (DE-588)4056995-0 |
| title | A Mathematical Theory of Evidence |
| title_auth | A Mathematical Theory of Evidence |
| title_exact_search | A Mathematical Theory of Evidence |
| title_exact_search_txtP | A Mathematical Theory of Evidence |
| title_full | A Mathematical Theory of Evidence Glenn Shafer |
| title_fullStr | A Mathematical Theory of Evidence Glenn Shafer |
| title_full_unstemmed | A Mathematical Theory of Evidence Glenn Shafer |
| title_short | A Mathematical Theory of Evidence |
| title_sort | a mathematical theory of evidence |
| topic | MATHEMATICS / History & Philosophy bisacsh Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie (DE-588)4395834-5 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | MATHEMATICS / History & Philosophy Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie Wahrscheinlichkeit Wahrscheinlichkeitsrechnung Statistik |
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