An Unforeseen Equivalence between Uncertainty and Entropy

Muller, Tim

Abstract

Uncertainty and entropy are related concepts, so we would expect there to be some overlap, but the equality that is shown in this paper is unexpected. In Beta models, interactions between agents are evidence used to construct Beta distributions. In models based on the Beta Model, such as Subjective Logic, uncertainty is defined to be inversely proportional to evidence. Entropy measures measure how much information is lacking in a distribution. Uncertainty was neither intended nor expected to be an entropy measure. We discover that a specific en-tropy measure (EDRB) coincides with uncertainty whenever uncertainty is defined. EDRB is the expected Kullback-Leibler divergence between two Bernouilli trials with parameters randomly selected from the distribution. EDRB allows us to apply the notion of uncertainty to other distributions that may occur in the context of Beta models.

Citation

Muller, T. (2019). An Unforeseen Equivalence between Uncertainty and Entropy

• Conference Name: 13th IFIP WG 11.11 International Conference on Trust Management
• Start Date: Jul 17, 2019
• End Date: Jul 19, 2019
• Acceptance Date: May 24, 2019
• Publication Date: Jul 19, 2019
• Deposit Date: Jul 8, 2019
• Publicly Available Date: Jul 8, 2019
• Public URL: https://nottingham-repository.worktribe.com/output/2142227
• Related Public URLs: http://ifiptm2019.compute.dtu.dk/IFIPTM19/IFIPTM.html