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 <[email protected]> wrote: > On Jun 21, 2013, at 2:48 PM, Ed Pozharski <[email protected]> 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
