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The max entropy distribution over (-oo,+oo) is usually taken to be either Gaussian or Laplace (two sided exponential), depending on moment conditions. There is
by hyperbovine 7y ago
The max entropy distribution over (-oo,+oo) is usually taken to be either Gaussian or Laplace (two sided exponential), depending on moment conditions. There is no such thing as a uniform distribution over the real line.
- baxtr 7y agoSide note: great how you spell infinity. Never saw this before. So simple and smart
- polyphonicist 7y agoCame here to say the same thing. Certainly haven't seen such depiction of infinity earlier. But this is a nice way. I am going to use it myself.
- mkl 7y agoIt's used as the symbol for infinity in Sympy, and probably other (and older) computer algebra systems.
- BenoitEssiambre 7y agoOf course there is. It's an improper prior (doesn't sum up to one), see link above. Theoretically the Gaussian is only maximum entropy given a mean and stddev. An infinite uniform is maxent without any knowledge of mean and stddev. In practice though you can use a wide Gaussian if it is more mathematically convenient and get about the same results.
- deleted 7y ago[deleted]
- hyperbovine 7y agoThe entropy of any improper prior diverges. There is no point in arguing over which one maximizes entropy; they all do, vacuously. Max entropy is not useful for discriminating amongst probability distributions unless you require them to actually be probability distributions.