[Ifeffit] fitting a specific k range

[Matt Newville]

Scott,

On Thu, Dec 5, 2013 at 11:18 AM, Scott Calvin <scalvin at sarahlawrence.edu> wrote:
> First, a disclaimer--I haven't looked at the data Matt sent (it's a busy time of year!), but I disagree in a general sense with my reading of what Bruce wrote (perhaps I am reading it wrong). In particular, I disagree with this statement:
>
>> Given that you are fitting in q-space, it is completely unreasonable (from a numerical perspective) to expect that the fit could possibly reproduce a feature that you have (intentionally or otherwise) filtered out of the data.
>>
>> To say that another way, given how you constructed the fit, you got a good fit.  You made the fit in a way that it cannot possibly reproduce the feature you are asking about, thus your question is ill-posed.
>
> To explain why, suppose I am fitting a standard--for the sake of a simple example, suppose it's copper. I include in my model paths out to 7 angstroms, including multiple-scattering paths, and use a Debye model for the MSRDs. It's possible to do a pretty good job in that kind of fit with just a few free parameters: S02, E0, an isotropic lattice expansion, and a Debye temperature. Now, suppose I perform the fit from 1 to 3.5 angstroms. Usually, the fit will do a pretty good job reproducing features well above 3.5 angstroms, because they're in the model (the paths are included) even though they're not in the fitting range. That's true for features in k-space that are caused by high-R paths too, of course.
>
> In fact, that kind of fit is particularly valuable to me, because it strongly suggests I've got the model right--I've essentially hid the high-R data from the numerical routines, so if it fits that region well anyway, it's probably because the model itself is a good one.
>
> While I defend that principle as a very important one, I'm not claiming it applies in Matt's case--it probably doesn't. To reproduce features at high-R, it IS necessary to have a model (i.e. paths) that cover the high-R contribution, and it sounds like Matt does not have those paths included in his model. But it's not necessary to FIT up to high R.

I agree that if a model fitted to data over some limited range of data
(either k or R, or even some external variable)  matches data well
outside that range, that is a good feature of the model.  But what if
it doesn't match the data outside that range?     As you say, model
that matches data over a very limited range can be useful, but mostly
in the context for how it extrapolates outside that range.

Back to Matt's point: using a sharp feature in chi(k) can be a
reasonable spectroscopic approach to identifying particular phases of
materials (mineral phases for example).    But to actually model any
of these sharp features in chi(k) would require a large R range for
the data, and might require many paths.   Trying to model such a
limited range while ignoring data outside that range is not a good
idea.

> P.S. My least favorite warning that Artemis provides is the one that tells you that you're including paths outside the fitting region, for just this reason. It's easy enough to change the preferences so that Artemis doesn't give that warning, and it's usually one of the first things I have my students do when they're first learning to fit.

When teaching students to drive a car is showing them how to put a
piece of electrical tape over the Check Engine light the first thing
you do?   Generally, false positives warnings are preferable to having
no warnings.

--Matt