Parker, Michael C and Jeynes, Chris (2023) A Maximum Entropy Resolution to the Wine/Water Paradox. Entropy, 25 (8). p. 1242. DOI https://doi.org/10.3390/e25081242
Parker, Michael C and Jeynes, Chris (2023) A Maximum Entropy Resolution to the Wine/Water Paradox. Entropy, 25 (8). p. 1242. DOI https://doi.org/10.3390/e25081242
Parker, Michael C and Jeynes, Chris (2023) A Maximum Entropy Resolution to the Wine/Water Paradox. Entropy, 25 (8). p. 1242. DOI https://doi.org/10.3390/e25081242
Abstract
The Principle of Indifference ('PI': the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the 'Wine/Water Paradox' as a resonant example of a 'Bertrand paradox', which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes using a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford's 'Law of Anomalous Numbers' (1938). We show that the PI should be understood to represent a family of informationally identical MaxEnt solutions, each solution being identified with its own explicitly justified boundary condition. In particular, our solution to the Wine/Water Paradox exploits Benford's Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics.
Item Type: | Article |
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Uncontrolled Keywords: | scale invariance; quantitative geometrical thermodynamics; Lagrange multipliers; Bayesian probability |
Subjects: | Z Bibliography. Library Science. Information Resources > ZZ OA Fund (articles) |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 18 Mar 2024 16:49 |
Last Modified: | 30 Oct 2024 21:12 |
URI: | http://repository.essex.ac.uk/id/eprint/37994 |
Available files
Filename: entropy-25-01242.pdf
Licence: Creative Commons: Attribution 4.0