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{Sorry if this is a silly question, but...} Is there a likelihood style approach to the problem of restraint weighting where the atomic co-ordinates are integrated out? In "Liking likelihood" (Acta D61 2169) there is an explanation of how to write the probability (or score) for a refinement in terms of a product of a chemical (restraints) part and an x-ray part. One can then write down a function which depends only on the restraint weights by integrating that probability over atomic co-ordinates? Optimise this in terms of the restraint weights and you have some indication what the weights should be for a particular model and dataset, at least close to the current model assuming you made some approximations when you integrated. In reciprocal space I thought you do something vaguely similar (integrating F/phi) to estimate weights for Fcalc/phicalc values (sigma-a/D etc)?
Has this been done already? Is there something horribly wrong with the idea? Simplistically I'd expect that poor data doesn't much care what restraint is applied as you can always get a good fit (due to parameters>observed), so paying more attention to the restraints comes out of the maths for giving a better overall score. Then for good data the weight which results will depend on whether or not you can fit the data ... if the restraints really cause a misfit of the x-ray data then they must need a lower weighting indicating there is something wrong with the restraint target values, or model.
Deciding on restraint weights also seems to be a longstanding problem in powder diffraction with small molecules, but in that case the weight to be applied depends on the dataset. The "chi^2" contributions from the x-ray and restraint terms need to be scaled to be of a similar order of magnitude in order to avoid ignoring one of the terms, but it is not clear exactly what the weighting should be. Is this likelihood style story the reasoning behind shelx's automatic determination of the restraint weighting?
Jon
