On Jun 21, 2013, at 8:36 AM, Ed Pozharski <epozh...@umaryland.edu> wrote:
> On 06/20/2013 01:07 PM, Douglas Theobald wrote: >> How can there be nothing "wrong" with something that is unphysical? >> Intensities cannot be negative. > > I think you are confusing two things - the true intensities and observed > intensities. But I'm not. Let me try to convince you ... > True intensities represent the number of photons that diffract off a crystal > in a specific direction or, for QED-minded, relative probabilities of a > single photon being found in a particular area of the detector when it's > probability wave function finally collapses. I agree. > True intensities certainly cannot be negative and in crystallographic method > they never are. They are represented by the best theoretical estimates > possible, Icalc. These are always positive. I also very much agree. > Observed intensities are the best estimates that we can come up with in an > experiment. I also agree with this, and this is the clincher. You are arguing that Ispot-Iback=Iobs is the best estimate we can come up with. I claim that is absurd. How are you quantifying "best"? Usually we have some sort of discrepancy measure between true and estimate, like RMSD, mean absolute distance, log distance, or somesuch. Here is the important point --- by any measure of discrepancy you care to use, the person who estimates Iobs as 0 when Iback>Ispot will *always*, in *every case*, beat the person who estimates Iobs with a negative value. This is an indisputable fact. > These are determined by integrating pixels around the spot where particular > reflection is expected to hit the detector. Unfortunately, science did not > yet invent a method that would allow to suspend a crystal in vacuum while > also removing all of the outside solvent. Neither we have included diffuse > scatter in our theoretical model. Because of that, full reflection intensity > contains background signal in addition to the Icalc. This background has to > be subtracted and what is perhaps the most useful form of observation is > Ispot-Iback=Iobs. How can that be the most useful form, when 0 is always a better estimate than a negative value, by any criterion? > These observed intensities can be negative because while their true > underlying value is positive, random errorsmay result in Iback>Ispot. There > is absolutely nothing unphysical here. Yes there is. The only way you can get a negative estimate is to make unphysical assumptions. Namely, the estimate Ispot-Iback=Iobs assumes that both the true value of I and the background noise come from a Gaussian distribution that is allowed to have negative values. Both of those assumptions are unphysical. > 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. > > In summary, there is indeed nothing wrong, imho, with negative Iobs. The > fact that some of these may become negative is correctly accounted for once > sigI is factored into the ML target. > > Cheers, > > Ed. > > -- > Oh, suddenly throwing a giraffe into a volcano to make water is crazy? > Julian, King of Lemurs >
