On Wednesday 06 June 2007, MarkBondin wrote:
2) What is the actual equation which defines the determinacy of a fitting procedure and does this differ between SS and MS analyses? For MS analyses there has been a recently published equation (Coord. Chem. Rev. 2005, 249, 141-160) which takes into acount the number of dimensions used in the analyses and is this only relevant to MS analyses of data? This has also been expressed in the paper by Binsted (Biochemistry. 1992, 31, 12117-12125) however a different equation has been detailed by Stern (Phys. Rev. B. 1993, 48, 9825-9827) which I have been using as a guide in my MS analyses. Is this acceptable?
1. I don't know what you mean by the word "determinacy". In any case, I thought I made it clear in my last post that, in my opinion, the differences between SS and MS analysis are in the physical interpretation and not in the statistical interpretation. Feff, Ifeffit, and Artemis certainly go to great lengths to downplay the differences between SS and MS paths in the context of the formalism of the theory and analysis, instead emphasizing their differences only in the context of physical interpretation. 2. Argonne's library only has access to the last year of Coord. Chem. Rev. and I don't have time this week to go fetch it from the stacks. So I cannot comment on that paper. 3. The paper by Stern should be read with some care. The argument Ed makes in that paper can only be true in the case of a perfectly packed signal. EXAFS data, although treated as signal processing problem, is never perfectly packed. The Nyquist criterion is an upper bound on the information content, but the actual content of the data is always somewhat less. There are some very fine papers by Rossner and Krappe about using Baysian techniques to find the actual information content of the EXAFS signal. The executive summary is that if think you need Ed's magic "+2", you are probably overusing the information content of your data. Most of us here in this list aren't as careful in practice as all that Baysian stuff. In general, one tries to stay "well below" the Nyquist upper bound. If your fitting parameters make sense physically, if the correlations are not "too high", and if the error bars on your parameters are not "too big", then you are probably not overusing the information content of your data. What is "too high" and "too big"? Well, I am purposefully using squishy language. It is kind of difficult to use Gaussian statistical techniques on EXAFS data, despite the fact that that's exactly what Ifeffit does. The reason is that Gaussin statistics presumes that your measurememt errors are statistical and normally distributed. In practice, exafs analysis is dominated by systematic uncertainties. Things like detector or sample non-linearities and the approximations made by Feff are much bigger sources of error than shot noise for most experiments. Most of those systematic problems are present in your analysis, but I have no idea how you could possibly quantify them. Hence I find myself using squishy language to discuss fit statistics. Read the papers by the frequent contributors to this mailing list. Scott Calvin and Shelly Kelly in particular are careful EXAFS practitioners who work on tough analysis problems and deal well with these issues. Doing what they do may not be as right as possible, but it certainly ain't wrong. HTH, B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/