TIm, I dare say that the goal is to get phases which match as good as > possible with what is inside the crystal. If this coincides with > maximising the likelihood, why don't we run refinement until the LL > stabilises? >
That's exactly what you should do: any optimisation procedure attains the correct solution only when changes in the parameters become 'insignificant' i.e. the optimisation is deemed to have converged. This corresponds to the extremum in the target function being attained so that the gradients w.r.t. the refined parameters become zero (within some margin of numerical precision), A very simple 1-parameter analogy is Hero's method to obtain the square root of a number (named after the 1st century Greek mathematician Hero of Alexandria though attributed to the Babylonians: http://en.wikipedia.org/wiki/Babylonian_method). This uses 'fixed-point iteration' to optimise the initial estimate X of sqrt(A) (X can be any positive number, the method has infinite radius of convergence): just replace X by the new estimate (X+A/X)/2 and iterate to convergence. So let's say I want sqrt(2): I make an initial guess of 1, so (1+2/1)/2 = 1.5, then (1.5+2/1.5)/2 = 1.4167 and keep iterating until the result doesn't change: only then will you have the correct answer. Since the target function in MX refinement is the total likelihood (working set + restraints), there's no reason whatsoever why any another function, such as Rfree & LLfree, should have an extremum at the same point in parameter space as the target function. Rfree is particular is problematic because it is unweighted, so poorly measured reflections in the test set are going to have a disproportionate influence on the result (e.g. see *Acta Cryst.* (1970). A*26*, 162). Cheers -- Ian
