[ccp4bb]: Statistical advice

["Eleanor J. Dodson" <ccp4@ysbl.york.ac.uk>]

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 Here is a statical problem at the heart of normalising isomorphous or
more seriously anomalous differences.

 such differences ideally represent 
FH cos(Phi_random) or 2F"H sin s(Phi_random) where 
Phi_random = PHI_protein-PHI_H


 Normalising them is rather iffy, but since
 <cos (Phi_random)> or <sin(Phi_random)> = 0.5 it is possible, and
anyway it seems to work!


 But we know that while the observed difference for any reflection
should approximate to the true difference with a associated sigma, the 
<absolute_value> will be an overestimate, at least for the weak
differences. 
 You can see this intuitively for those reflections which should have
difference = 0; since each observation has an associated Sigma, the rms
value will be > 0.0.

 Can anyone suggest a way to weight down the observed difference to take
this problem into account. 
 Lets assume as a simplification that the F is distributed with a normal
distribution with known Sigma, and that the 2 measurements , FP and FPH
or F(+) and F(-) are independent.. 
I think that this means that the abs(difference) will follow a Poisson
distribution, but I am not sure how to use the associated error tables.
  
 No prizes for the best answer, but it will improve the behaviour of
many programs, difference pattersons and Ecalc in particular! 
  Eleanor Dodson  

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Eleanor J.Dodson, Chemistry Department, University of York, U.K.
Tel: Home +44 (1904) 42 44 49, work:  +44 (1904) 43 25 65
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