[SciPy-User] scipy.stats.fit inquiry
Sat Oct 24 05:45:28 CDT 2009
I think that in essence it is even simpler than that. It is a Poisson
Likelihood objective function, reformatted so that its difference when
changing models behaves like a chi2 in the limit of large enough counts.
Note that it is perfectly fine for unbinned analysis, contrary to what
could be inferred from the Sherpa discussion. Roughly speaking, because
it behaves well at very small counts per bin, you can go without trouble
to the limit of one or zero count per bin, which is actually unbinned....
We use it extensively in gamma-ray astrophysics, especially with the
Fermi observatory (http://fermi.gsfc.nasa.gov/).
Anne Archibald wrote:
> 2009/10/20 <email@example.com>:
>> I never heard about the Cash statistic.
> It's a clever trick for estimating uncertainties on fitted parameters;
> you do some magic with the likelihood ratio and you get statistic that
> behaves like chi-squared, apart from being exactly zero at your
> best-fit value. So it's no use for esstimating quality-of-fit, but you
> can use it to get error regions just the way you would if you'd had
> Gaussian statistics and a chi-squared fit. (Cash 1979, "Parameter
> estimation in astronomy through application of the likelihood ratio")
> Incidentally, I have some code implementing the Kuiper test, a
> modified K-S test that is sensitive to different aspects of the shape
> of the distribution, and (more importantly for me) is invariant on
> shifting a distribution or sample modulo 1. I haven't submitted it for
> inclusion because the interface I used is a little different from that
> used by scipy's K-S test, but if there's interest I'd be happy to
> contribute it.
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