Abstract
In a recent PRL (2013, 111, 180604), we invoked the Shore and Johnson axioms which demonstrate that the least-biased way to infer probability distributions fpig from data is to maximize the Boltzmann-Gibbs entropy. We then showed which biases are introduced in models obtained by maximizing nonadditive entropies. A rebuttal of our work appears in entropy (2015, 17, 2853) and argues that the Shore and Johnson axioms are inapplicable to a wide class of complex systems. Here we highlight the errors in this reasoning.
Highlights
In a recent PRL (2013, 111, 180604), we invoked the Shore and Johnson axioms which demonstrate that the least-biased way to infer probability distributions {pi } from data is to maximize the Boltzmann-Gibbs entropy
Tsallis contends that “nonadditive entropies emerge from strong correlations which are definitively out of the Shore and Johnson (SJ) hypothesis” adding that the
Tsallis asserts that “We see that the SJ set of axioms, demanding, as they do, system independence, are not applicable unless we have indisputable reasons to believe that the data that we are facing correspond to a case belonging to the exponential class, and by no means correspond to strongly correlated cases such as those belonging to the power-law or stretched-exponential classes, or even others”
Summary
In a recent PRL (2013, 111, 180604), we invoked the Shore and Johnson axioms which demonstrate that the least-biased way to infer probability distributions {pi } from data is to maximize the Boltzmann-Gibbs entropy. I (or any function that is monotonic with this entropy), under constraints where qi is the prior distribution on pi that contains any foreknowledge of the system.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
