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
