Jon's right - when the counts are very low - i.e. zeroes and ones around - then the correct Bayesian approach is to use Poisson statistics. This, as Jon said, has been tackled by Antoniadis et al. (Acta Cryst. (1990). A46, 692-711 Maximum-likelihood methods in powder diffraction refinements, A. Antoniadis, J. Berruyer and A. Filhol) in the context of the Rietveld method some years ago. This paper is very informative for those who are intrigued about the fact that you can do anything when diffraction patterns have lots of zeroes and ones around. Curiously, the weighting ends up having as much to do with the model value (which can, of course, be non-integer) as the data. Devinder Sivia's excellent OUP monograph, "Data Analysis: a Bayesian Tutorial" (http://www.oup.co.uk/isbn/0-19-856832-0) discusses all of this in a very readable way.
Bill
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]
Sent: 12 October 2006 00:37
To: rietveld_l@ill.fr
Subject: Re: About zero counts etc.
Hello Joerg,
> -Having measured n counts, the estimated value is n+1
You might have a hard time convincing me on that one.
> -Having measured n counts, the esd is also sqrt(n+1)!
If n is zero then spending more time on the data collection might be better than
more time on the analysis.
> Things change with variable counting times.
id31sum uses counts=counts and esd=sqrt(counts+alp) where alp=0.5 is the default
and can be overridden on the command line. Perhaps there aren't many people who
use that option. Should we change the default? The 0.5 came from the literature
but it was some time ago and I can't remember where. In any case it then gets
convoluted with the monitor error. Sqrt(n+1) gives a very low chi^2 if the
actual background is 0.1 (eg: 1 count every 10 datapoints). Might be better to
just use the Poisson itself, as in abfit [1].
> the above correction for the estimated
> values gave significant better R values.
Are you using background subtracted R-values? If only R-values were significant.
Jon
[1] Acta Cryst. (1990). A46, 692-711
Maximum-likelihood methods in powder diffraction refinements
A. Antoniadis, J. Berruyer and A. Filhol
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