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How comprehensive is the following book - What interpretations are missing? Interpretations of Probability, Andrei Khrennikov, 2009, de Gruyter, ISBN 978-3-11-020748-4 http://www.degruyter.com/cont/fb/ma/detailEn.cfm?isbn=9783110207484&sel=pi Contents:http://www.degruyter.com/files/pdf/9783110207484Contents.pdf |
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Though quantum probability and negative probability models are quite interesting, this is hardly exhaustive of nonstandard models of probability. There are for instance, imprecise probability models, and models that violate Kolmogorov's countable additivity axiom, and more. As an aside, the book may be more properly called 'Models of Probability'. Interpretations of probability, generally involve characterizing the competing understandings of probability as logically prescribed values, limiting frequencies, propensities, subjective beliefs, etc. Models, or axiomatizations can certainly be motivated by these understandings, but the problem of creating a variant system is different than arguing for a particular interpretation. |
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