Re:Why isn't everything normally distributed?
by theoh on Thursday July 20, 2017 @08:59PM
(#14817376)
When you want to fit a distribution to a star's image on the plate, normal does indeed seem a weird choice. But the point about multidimensional gaussians is that they are the only distribution that is maximally "ignorant" (maximum entropy) -- so if there's a small (unresolvable) companion star we don't know about, we can do no better than a gaussian if we want to ignore it.
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Re:Why isn't everything normally distributed?
by antognini on Thursday July 20, 2017 @09:13PM
(#14817406)
Well, that's not quite true. The normal distribution maximizes entropy for a finite mean and variance. But it's not guaranteed that certain physical processes have well defined means and variances. A power law is the maximum entropy distribution with a well defined mean, but undefined variance, on the range (0, infinity). [1]
Of course in reality, at some point, some other physical process starts to dominate and cuts off the power law. this then turns it into a power law with a different slope or an exponential cutoff.
Edit: I forgot to add that a star's light profile on an image is actually approximately Gaussian. But it isn't exactly Gaussian --- I seem to remember that the core more closely resembles a Lorentzian. I am obviously not an observer, otherwise I would have thought of that immediately!
[1]: https://en.wikipedia.org/wiki/Maximum_entropy_probability_di...
> A power law is the maximum entropy distribution with a well defined mean, but undefined variance, on the range (0, infinity).
The maximum entropy distribution with a given mean is the exponential. I think to define power law distributions you will need additional constraints more concrete than "undefined variance".
Re:Why isn't everything normally distributed?
by antognini on Friday July 21, 2017 @11:09AM
(#14821127)
That's if you require the range to be [0, infinity). If you don't require 0 to be a valid point in the distribution then a power law is the maximum entropy distribution. A power law just diverges if you try to integrate to zero, so you have to find a lower entropy distribution.