<div class="gmail_quote">On Sat, Nov 19, 2011 at 11:20 PM, Pavel Afonine <span dir="ltr"><<a href="mailto:pafonine@lbl.gov" target="_blank">pafonine@lbl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<u></u>
<div bgcolor="#ffffff" text="#000000"><div>
<br>
<blockquote type="cite">
<div class="gmail_quote">
<div>The method of using the ratio of gradients doesn't make
sense in a maximum likelihood context, <br>
</div>
</div>
</blockquote>
<br></div>assuming that by "a maximum likelihood context" you mean refinement
using a maximum-likelihood (ML) criterion as X-ray term (or, more
generally, I would call it experimental data term, as it can be
neutron too, for instance), I find the whole statement above as a
little bit strange since it mixes different and absolutely not
related things: type of crystallographic data term and a method of
relative scale (weight) determination between it and the other term
(restraints). <br>
<br>
I don't see how the choice of crystallographic data term (LS, ML,
real-space or any other) is related to the method of this scale
determination.<br>
<br></div></blockquote><div><br>This shouldn't be a surprise - in short, the errors are used as weights in LS and ML optimization targets, the latter just uses a different form for the errors that estimates all the model and unmeasured uncertainties (like phase error).� So if the data is poorly predicted by a model, the ML target is broader/flatter (as are the gradients!), while good/complete models will yield a sharper ML target.� So the likelihood target is naturally weighted, in a sense.� This doesn't happen with least squares (unless the weights are not the inverse variances, which seems to be what the MLMF paper you mentioned is doing?).<br>
<br>The likelihood function can then be plugged in to Bayes' law - if the model and data error terms are all accounted for, no other weighting should be necessary.� This is discussed in Airlie McCoy's excellent review (<font size="2"><a href="http://dx.doi.org/10.1107/S0907444904016038" target="_blank">http://dx.doi.org/10.1107/S0907444904016038</a></font>) - see sections 4.4 and 4.6, and the derivation is also in <a href="http://dx.doi.org/10.1107/S0907444911039060">http://dx.doi.org/10.1107/S0907444911039060</a><br>
�</div>Hope this helps!<br>Regards,<br>Tim<br><br>
</div>