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Is Shannon Entropy subjective?

  1. Jan 24, 2016 #1
    If you have multiple possible states of a system then the Shannon entropy depends upon whether the outcomes have equal probability. A predictable outcome isn't very informative after all. But this seems to rely on the predictive ability of the system making the observation/measurement. This suggests that the amount of Shannon entropy of a system depends on who you ask.
     
    Last edited: Jan 24, 2016
  2. jcsd
  3. Jan 24, 2016 #2

    Dale

    Staff: Mentor

    Especially if you ask a Bayesian or a frequentist.
     
  4. Jan 25, 2016 #3

    chiro

    User Avatar
    Science Advisor

    The normal Shannon entropy for a discrete state system gives a person an idea of the information density or content of that system.

    The more random a system is the more information is needed to describe that system. If you have a system with so much entropy and information with so much entropy then the information will decrease the uncertainty of the system itself.

    Also realize that entropy - like anything else in mathematics and language in particular has a basis.

    You can all sorts of entropies corresponding to the distribution you are looking at - and that includes all possible conditional distributions.

    The entropy measures are distribution invariant (as long as they have a finite sample space for the proper entropies) and have a lot of algebraic constraints that are mathematically consistent and consistent probabilistically.
     
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