ISIS and its fit statistics

From: FIll Humphrey <phumphrey_at_email.domain.hidden>
Date: Fri, 30 Jan 2004 10:12:24 -0800 (PST)
To whom it may concern...

		Please excuse the formal greeting of this email... I have 
a couple of queries/ comments regarding ISIS and its computation of the 
fit statistics for (broad-band) spectral analysis. I've poked around the 
source code to see if I could figure these out/ sort them out myself, but 
I was wondering if anyone slightly more knowledgeable than myself on such 
matters would know if I'm just being naiive:

1. In the computation of the cash statistic (cash.c in the code?), I've 
run into a serious issue if the model in any bin hits zero. To whit, in 
the code as I read it, if the model (is that what fxi is?) goes to zero 
but the data is >0.0, this seems to contribute a significant negative term 
to the fit statistic since the log(fxi/yi) term is not added on to the 
data. I understood that this term should in fact be added, since it will 
go to -\infty and the fit statistic will inflate (the opposite sense to 
what it does). With poor-quality data, this has led to fits where the 
model normalization hitting zero is the preferred one! I did a quick fix 
by putting a hard lower-limit (of 1E-5) on both yi and fxi (and 
recompiling), which seemed to do the trick. Does anyone know if this is 
sensible/ if I'm totally misunderstanding it? If I'm right, perhaps this 
could be fixed in the next ISIS release?

2. For both the Cash and \chi^2 fit statistics, to my very inexperienced 
reading of the code, neither seem to take into account the errors on the 
background you read in. Is this correct? I've noticed tangible differences 
between fits done with XSPEC and ISIS, and was wondering if this is the 
root of the discrepancy. If the background's not taken into account, would 
it be possible to deal with it à la XSPEC? 

Sorry the email's so long. Thanks for any comments anyone might have.

	Regards,
		Fill Humphrey

-- 
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Fill Humphrey                             email: phumphre_at_email.domain.hiddenDepartment of Physics and Astronomy,             phumphrey_at_email.domain.hiddenUniversity of California, Irvine,          tel: +1 949 824 3013
4129 Frederick Reines Hall           Dept. Fax: +1 949 824 2174
Irvine, CA 92697-4575
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Received on Fri Jan 30 2004 - 13:35:20 EST

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