Re: re. Maximum Likelihood

[David Watkin <david.watkin@chemistry.oxford.ac.uk>]

Many thanks for the swift reply - I hadn't really wanted to bother you 
with what was probably a simple problem for folk in the know.  In fact, 
since e-mailing Ton (and the reset of the world!) this morning, I 
re-read most of your web lectures, and then Luzzati's 1952 paper.  He 
alludes to your conclusion on page 807.

Best wishes
				David

Randy Read wrote:
> 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.
>