Re: ISIS: loading data with proper statistical error

On Nov 30, 2012, at 12:49 PM, Nicolas Barrière wrote:

> Now, and it's a whole different discussion, how do you think I should calculate these errors?
> A lot of bins contain less that 10 counts, so Gaussian statistics (sqrt(N)) would be totally underestimated. 
> Poisson statistics would be more correct. Is there a build-in function to calculate the errors (something like what Gherels (1986) described)?
> 
> With Poisson errors in each bin, should I worry when I rebin the data that the errors will end up over-estimated?

If your concern in your last question is whether in rebinning, errors are propagated by 
something like adding quadrature, don't worry, they're not (unless you write that
yourself).

See the help file for "set_fit_statistic".  You get the usual choice of Chi^2 by data
(i.e., Gaussian, the default), Chi^2 by model, Gehrels, Cash, Least Squares.  

In rebinning, ISIS calculates the new counts in the new bin, and then calculates the 
new error from that. So, for example, in the Gehrels formula of:

	1 + sqrt(Counts+0.75)

you only get that 1 & 0.75 once, not in quadrature from all the bins that made up the 
new bin.  Counts is the rebinned counts.

I usually use straight sqrt(Counts), i.e., the default.  I'm less religious about trying to 
never  bin data and trying to worry too much about going into the low counts regime.  
But I  tend to look at bright things, and I tend to worry more about instrumental effects 
(in  which case binning is good, under the hope that one averages out systematics to 
some degree).

The few times I don't end up binning, I usually use the Cash statistic.

Cheers,

Mike





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