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Re: re. Maximum Likelihood

On Thursday 05 December 2002 12:55, you wrote:
> Ton
> 	Did you ever hear of anyone trying to refine small molecule structures
> using maximum likelihood?  I one heard Randy Read suggest that it would
> be of little value, but wondered what evidence he had.
>
> Best wishes
> 		David

Hi,

I think there are two issues with applying maximum likelihood to refining 
small molecule structures.  The first is the practical one of determining
Sigma(A) values from cross-validation data.  There aren't enough reflections 
in a typical small molecule data set to give up hundreds of them just to 
calibrate the likelihood functions.  So it would probably be necessary to 
determine the Sigma(A) values with the working data.  That would be fine if 
the observation to parameter ratio was high enough that there wasn't much 
over-fitting of the data.  But at that point the data would be to atomic 
resolution and the structures could be refined to agree with the data nearly 
as well as you'd expect from measurement error.  In the limit of the 
disagreement essentially coming from measurement error, the maximum 
likelihood target reduces to a least-squares target.  This can be seen from 
the form of the MLF1 target, which is a Gaussian approximation to the 
likelihood function.

So in practice I think the impact would be much less than we've seen in 
macromolecular crystallography.

As for hard evidence, I don't have any, not having actually tried it.  It 
could be interesting to see what happened.  If you wanted to try it, the MLF1 
target might be the easiest to introduce into a least-squares program, since 
it's Gaussian in form.

-- 

Randy J. Read
Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research      Tel: + 44 1223 336500
Wellcome Trust/MRC Building                   Fax: + 44 1223 336827
Hills Road                                    E-mail: rjr27@cam.ac.uk
Cambridge CB2 2XY, U.K.                       www-structmed.cimr.cam.ac.uk

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