Re: systematic errors

On Jul 31, 2009, at 8:52 AM, gulabd_at_email.domain.hidden
> I have a situation where background level is determined with a  
> systematic uncertainty of a few percent. So ideally I should  
> increase the error bars associated with background by applying  
> systematic errors to the background spectrum.
>
> XSPEC12 can read systematic errors from the background PHA file. I  
> can see the differences in the reduced chi^2 with and without the  
> systematic errors applied to the background file with grppha.
>
> It seems ISIS can read systematic errors only from the source(+back)  
> PHA file.

Who knew...  I have done things like vary the level of the background  
during the fits.  (I have actually been using in ISIS my own variation  
of the XSPEC "corrfile" procedure, except that the normalization  
constant could be varied during the fit, not iteratively between  
fits.  Took XSPEC several years more before they changed their  
functionality to allow that.)  But I've never tried to increase the  
error bars.  But thinking out loud here, we have,

	\Delta C^2 = C +  S_d/S_b * B_s + (F_d*C)^2 + (F_b*B_s)^2

where \Delta C^2 is the variance on the data counts, C is the counts,  
S_d is the data backscale*data exposure, S_b is the background  
backscale*data exposure, B_s is the scaled background, F_d is the  
fractional systematic errors on the data, F_b is the fractional  
systematic errors on the background.  So, rewriting:

	\Delta C^2 = C +  S_d/S_b * B_s + [ (F_d)^2 + (F_b*B_s/C)^2]*C^2

If you tell ISIS to set the *data* systematic errors to sqrt( F_d^2 +  
(F_b*B_s/C)^2 ), then you should get exactly the thing you want.

So, I know that we could do:

isis>  fd = get_sys_err_frac(data_id);
isis> c = get_data_counts(data_id);
isis> bs = get_back  % This is the scaled background

and that's three of the pieces you need.  I think if you define the  
background as a file, e.g.,

isis> bid = load_data("bakcground.pha");
isis> fb = get_sys_err_frac(bid);

Then you could do:

isis> set_sys_err_frac( data_id, sqrt(fd^2+ (fb*bs/c)^2));
isis> delete_data(bid);  % You no longer need that as data, so drop it.

Now, since this is totally off the top of my head, I haven't tried  
this at all.  You'd have to be careful about making sure all the  
arrays were the same length, you were dividing through by 0's, etc.,  
etc.  But with a little bit of effort, it seems like you could write a  
dozen line script or so which would do this the way you wanted for any  
data set.

Cheers,

Mike


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