A Mathematical Theory of Evidence by Glenn Shafer (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Classic text on evidence theory. Readers would be well advised to have a background in set theory, Choquet theory, and information uncertainty before reading the text as it assumes a great deal of awareness/background in the foundation theory. If you have a decent grasp of the underlying structure the book is a strong manuscript which belongs on your shelf if your interests/needs lie in this direction.Uncertainty and Information by George Klir[…]andA Mathematical Theory of Hints – An Approach to the Dempster-Shafer Theory of Evidence by Monney[…] or buy at Amazonare both recommended texts of related reading.

⭐I find the same book in my library. It is a classical book, but not easy to understand. And what is more, the book delivery comes too late.

⭐Interesting… Although I didn’t found enough explanation for why Dempster-Shafer belief is totally monotone… It is reasonable, because it is the first book of their theory~~

⭐Es handelt sich um eine gute klassische Einführung in das Thema von Erfinder selbst. Eignet sich zur Vertiefung in dises Thema für Interessierte in der Expertensystemprogrammierung.

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