I hope I am not duplicating too much of this fascinating discussion with these comments: perhaps the main reason there is confusion about what to do is that neither F nor I is really the most suitable thing to use in refinement. As pointed out several times in different ways, we don't measure F or I, we only measure counts on a detector. As a convenience, we "process" our diffraction images to estimate I or F and their uncertainties and model these uncertainties as simple functions (e.g., a Gaussian). There is no need in principle to do that, and if we were to refine instead against the raw image data these issues about positivity would disappear and our structures might even be a little better.
Our standard procedure is to estimate F or I from counts on the detector, then to use these estimates of F or I in refinement. This is not so easy to do right because F or I contain many terms coming from many pixels and it is hard to model their statistics in detail. Further, attempts we make to estimate either F or I as physically plausible values (e.g., using the fact that they are not negative) will generally be biased (the values after correction will generally be systematically low or systematically high, as is true for the French and Wilson correction and as would be true for the truncation of I at zero or above). Randy's method for intensity refinement is an improvement because the statistics are treated more fully than just using an estimate of F or I and assuming its uncertainty has a simple distribution. So why not avoid all the problems with modeling the statistics of processed data and instead refine against the raw data. From the structural model you calculate F, from F and a detailed model of the experiment (the same model that is currently used in data processing) you calculate the counts expected on each pixel. Then you calculate the likelihood of the data given your models of the structure and of the experiment. This would have lots of benefits because it would allow improved descriptions of the experiment (decay, absorption, detector sensitivity, diffuse scattering and other "background" on the images,....on and on) that could lead to more accurate structures in the end. Of course there are some minor issues about putting all this in computer memory for refinement.... -Tom T ________________________________________ From: CCP4 bulletin board [CCP4BB@JISCMAIL.AC.UK] on behalf of Phil [p...@mrc-lmb.cam.ac.uk] Sent: Friday, June 21, 2013 2:50 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] ctruncate bug? However you decide to argue the point, you must consider _all_ the observations of a reflection (replicates and symmetry related) together when you infer Itrue or F etc, otherwise you will bias the result even more. Thus you cannot (easily) do it during integration Phil Sent from my iPad On 21 Jun 2013, at 20:30, Douglas Theobald <dtheob...@brandeis.edu> wrote: > On Jun 21, 2013, at 2:48 PM, Ed Pozharski <epozh...@umaryland.edu> wrote: > >> Douglas, >>>> 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. >> >> First off, you may find it useful to avoid such words as absurd and >> indisputable fact. I know political correctness may be sometimes overrated, >> but if you actually plan to have meaningful discussion, let's assume that >> everyone responding to your posts is just trying to help figure this out. > > I apologize for offending and using the strong words --- my intention was not > to offend. This is just how I talk when brainstorming with my colleagues > around a blackboard, but of course then you can see that I smile when I say > it. > >> To address your point, you are right that J=0 is closer to "true intensity" >> then a negative value. The problem is that we are not after a single >> intensity, but rather all of them, as they all contribute to electron >> density reconstruction. If you replace negative Iobs with E(J), you would >> systematically inflate the averages, which may turn problematic in some >> cases. > > So, I get the point. But even then, using any reasonable criterion, the > whole estimated dataset will be closer to the true data if you set all > "negative" intensity estimates to 0. > >> It is probably better to stick with "raw intensities" and construct >> theoretical predictions properly to account for their properties. >> >> What I was trying to tell you is that observed intensities is what we get >> from experiment. > > But they are not what you get from the detector. The detector spits out a > positive value for what's inside the spot. It is we, as human agents, who > later manipulate and massage that data value by subtracting the background > estimate. A value that has been subjected to a crude background subtraction > is not the raw experimental value. It has been modified, and there must be > some logic to why we massage the data in that particular manner. I agree, of > course, that the background should be accounted for somehow. But why just > subtract it away? There are other ways to massage the data --- see my other > post to Ian. My argument is that however we massage the experimentally > observed value should be physically informed, and allowing negative intensity > estimates violates the basic physics. > > [snip] > >>>> 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. >> >> See, I have a problem with this. Both common sense and laws of physics >> dictate that number of photons hitting spot on a detector is a positive >> number. There is no law of physics that dictates that under no >> circumstances there could be Ispot<Iback. > > That's not what I'm saying. Sure, Ispot can be less than Iback randomly. > That does not mean we have to estimate the detected intensity as negative, > after accounting for background. > >> Yes, E(Ispot)>=E(Iback). Yes, E(Ispot-Iback)>=0. But P(Ispot-Iback=0)>0, >> and therefore experimental sampling of Ispot-Iback is bound to occasionally >> produce negative values. What law of physics is broken when for a given >> reflection total number of photons in spot pixels is less that total number >> of photons in equal number of pixels in the surrounding background mask? >> >> Cheers, >> >> Ed. >> >> -- >> Oh, suddenly throwing a giraffe into a volcano to make water is crazy? >> Julian, King of Lemurs
