On 21 June 2013 13:36, Ed Pozharski <epozh...@umaryland.edu> wrote: > Replacing Iobs with E(J) is not only unnecessary, it's ill-advised as it > will distort intensity statistics. For example, let's say you have > translational NCS aligned with crystallographic axes, and hence some set of > reflections is systematically absent. If all is well, <Iobs>~0 for the > subset while <E(J)> is systematically positive. This obviously happens > because the standard Wilson prior is wrong for these reflections, but I > digress, as usual. >
Ed, If you observe the symptoms of translational NCS in the diffraction pattern (i.e. systematically weak zones of reflections) you must take it into account when calculating the averages, i.e. if you do it properly parity groups should be normalised separately (though I concede there may be a practical issue in that I'm not aware of any software that currently has this feature). In that case <E(J)> will be ~ 0, as expected. If you don't do that then clearly you can't expect to get the right answer! The theoretical intensities are based on the assumption that the intensity distributions are all positive, so it makes no sense to compare them with an experimental distribution where a significant fraction are negative. How exactly do you propose to deal properly with the P-Y L test that I described? - because of course that also inherently assumes that the intensities are all positive and it's certainly not valid to assume that E(J) = E(F)^2 ! Another point is that (to paraphrase G. Orwell) "not all reflections are created equal, just some are more equal than others". What I mean is that in counting reflections for the cumulative distributions (i.e. you count the number of reflections in ranges of intensity or in ranges of L), a weak reflection should be counted as fractional with a contribution to the total which is less than 1, on a continuous scale from 0 to 1 related to I/sigma(I). In fact referring to your original posting reflections with h < -4 will get such a small weight that it will be effectively zero and they won't be counted at all (or it won't make the slightest difference whether you count them or not). Of course when it comes to outputting reflections you can't have a fractional reflection, it's either included or it isn't. So then you may have to have an arbitrary cutoff, though such reflections would likely end up with zero intensity and large SD (but the programs may not currently be good at estimating the latter in such a situation, which is probably why they are currently rejected). Another point worth mentioning is that the observed distributions of E^n (E = normalised structure amplitude) tend to be very noisy, particularly for large n, and I have a suspicion (as yet untested) that this may come from weak reflections which have made a full contribution to the count when it should have been fractional (or even zero). I'm currently working on a revised version of TRUNCATE where some or all of the above issues will be addressed. Cheers -- Ian
