[Ifeffit] Asymmetric error bars in IFeffit

[Matt Newville]

Hi Scott,

That's a pretty amazing use case.

But I'm not sure I understand the issue exactly right.   I would have
thought the volume (r**3) was the important physical parameter, and
that a 1000nm particle would dominate the spectra over 3nm particles.
   Or is it that you are trying to distinguish between 1 very large
crystal  or 100s of smaller crystals?   Perhaps the effect you're
really trying to account for is the surface/volume ratio?  If so, I
think using Matthew Marcus's suggestion of using 1/r (with a safety
margin) makes the most sense.

--Matt

On Fri, Oct 22, 2010 at 3:23 PM, Scott Calvin <dr.scott.calvin at gmail.com> wrote:
> Hi all,
> I'm puzzling over an issue with my latest analysis, and it seemed like the
> sort of thing where this mailing list might have some good ideas.
> First, a little background on the analysis. It is a simultaneous fit to four
> samples, made of various combinations of three phases. Mossbauer has
> established which samples include which phases. One of the phases itself has
> two crystallographically inequivalent  absorbing sites. The result is that
> the fit includes 12 Feff calculations, four data sets, and 1000 paths.
> Remarkably, everything works quite well, yielding a satisfying and
> informative fit. Depending on the details, the fit takes about 90 minutes to
> run. Kudos to Ifeffit and Horae for making such a thing possible!
> Several of the parameters that the fit finds are "characteristic crystallite
> radii" for the individual phases. In my published fits, I often include a
> factor that accounts for the fact that a phase is nanoscale in a crude way:
> it assumes the phase is present as spheres of uniform radius and applies a
> suppression factor to the coordination numbers of the paths as a function of
> that radius and of the absorber-scatterer distance. Even though this model
> is rarely strictly correct in terms of morphology and size dispersion, it
> gives a first-order approximation to the effect of the reduced coordination
> numbers found in nanoscale materials. Some people, notably Anatoly Frenkel,
> have published models which deal with this effect much more realistically.
> But those techniques also require more fitted variables and work best with
> fairly well-behaved samples. I tend to work with "messy" chemical samples of
> free nanoparticles where the assumption of sphericity isn't terrible, and
> the size dispersion is difficult to model accurately.
> At any rate, the project I'm currently working on includes a fitted
> characteristic radius of the type I've described for each of the phases in
> each of the samples. And again, it seems to work pretty well, yielding
> values that are plausible and largely stable.
> That's the background information. Now for my question:
> The effect of the characteristic radius on the spectrum is a strongly
> nonlinear function of that radius. For example, the difference between the
> EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination
> number effect is completely negligible. The difference between 1 nm and 10
> nm crystals, however, is huge.
> So for very small crystallites, IFeffit reports perfectly reasonable error
> bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger
> crystallites, however, it tends to report values like 10 +/- 500 nm. I
> understand why it does that: it's evaluating how much the parameter would
> have to change by to have a given impact on the chi square of the fit. And
> it turns out that once you get to about 10 nm, the size could go arbitrarily
> higher than that and not change the spectrum much at all. But it couldn't go
> that much lower without affecting the spectrum. So what IFeffit means is
> something like "the best fit value is 10 nm, and it is probable that the
> value is at least 4 nm." But it's operating under the assumption that the
> dependence of chi-square on the parameter is parabolic, so it comes up with
> a compromise between a 6 nm error bar on the low side and an infinitely
> large error bar on the high side. Compromising with infinity, however,
> rarely yields sensible results.
> Thus my question is if anyone can think of a way to extract some sense of
> these asymmetric error bars from IFeffit. Here are possibilities I've
> considered:
> --Fit something like the log of the characteristic radius, rather than the
> radius itself. That creates an asymmetric error bar for the radius, but the
> asymmetry the new error bar possesses has no relationship to the uncertainty
> it "should" possess. This seems to me like it's just a way of sweeping the
> problem under the rug and is potentially misleading.
> --Rerun the fits setting the variable in question to different values to
> probe how far up or down it can go and have the same effect on the fit. But
> since I've got nine of these factors, and each fit takes more than an hour,
> the computer time required seems prohibitive!
> --Somehow parameterize the guessed variable so that it does tend to have
> symmetric error bars, and then calculate the characteristic radius and its
> error bars from that. But it's not at all clear what that parameterization
> would be.
> --Ask the IFeffit mailing list for ideas!
> Thanks!
> --Scott Calvin
> Sarah Lawrence College
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