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Title: A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits

Abstract

A general problem when fitting EXAFS data is determining whether particular parameters are statistically significant. The F-test is an excellent way of determining relevancy in EXAFS because it only relies on the ratio of the fit residual of two possible models, and therefore the data errors approximately cancel. Although this test is widely used in crystallography (there, it is often called a ''Hamilton test'') and has been properly applied to EXAFS data in the past, it is very rarely applied in EXAFS analysis. We have implemented a variation of the F-test adapted for EXAFS data analysis in the RSXAP analysis package, and demonstrate its applicability with a few examples, including determining whether a particular scattering shell is warranted, and differentiating between two possible species or two possible structures in a given shell.

Authors:
 [1];  [2]; ;  [3];  [1]
  1. Physics Department, University of California, Santa Cruz, California 95060 (United States)
  2. (United States)
  3. Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
Publication Date:
OSTI Identifier:
21054572
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 882; Journal Issue: 1; Conference: XAFS13: 13. international conference on X-ray absorption fine structure, Stanford, CA (United States), 9-14 Jul 2006; Other Information: DOI: 10.1063/1.2644450; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ABSORPTION SPECTROSCOPY; CRYSTAL STRUCTURE; CRYSTALLOGRAPHY; DATA ANALYSIS; ERRORS; FINE STRUCTURE; SCATTERING; TESTING; VARIATIONS; X-RAY SPECTROSCOPY

Citation Formats

Downward, L., Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, Booth, C. H., Lukens, W. W., and Bridges, F.. A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits. United States: N. p., 2007. Web. doi:10.1063/1.2644450.
Downward, L., Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, Booth, C. H., Lukens, W. W., & Bridges, F.. A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits. United States. doi:10.1063/1.2644450.
Downward, L., Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, Booth, C. H., Lukens, W. W., and Bridges, F.. Fri . "A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits". United States. doi:10.1063/1.2644450.
@article{osti_21054572,
title = {A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits},
author = {Downward, L. and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 and Booth, C. H. and Lukens, W. W. and Bridges, F.},
abstractNote = {A general problem when fitting EXAFS data is determining whether particular parameters are statistically significant. The F-test is an excellent way of determining relevancy in EXAFS because it only relies on the ratio of the fit residual of two possible models, and therefore the data errors approximately cancel. Although this test is widely used in crystallography (there, it is often called a ''Hamilton test'') and has been properly applied to EXAFS data in the past, it is very rarely applied in EXAFS analysis. We have implemented a variation of the F-test adapted for EXAFS data analysis in the RSXAP analysis package, and demonstrate its applicability with a few examples, including determining whether a particular scattering shell is warranted, and differentiating between two possible species or two possible structures in a given shell.},
doi = {10.1063/1.2644450},
journal = {AIP Conference Proceedings},
number = 1,
volume = 882,
place = {United States},
year = {Fri Feb 02 00:00:00 EST 2007},
month = {Fri Feb 02 00:00:00 EST 2007}
}
  • A general problem when fitting EXAFS data is determining whether particular parameters are statistically significant. The F-test is an excellent way of determining relevance in EXAFS because it only relies on the ratio of the fit residual of two possible models, and therefore the data errors approximately cancel. Although this test is widely used in crystallography (there, it is often called a 'Hamilton test') and has been properly applied to EXAFS data in the past, it is very rarely applied in EXAFS analysis. We have implemented a variation of the F-test adapted for EXAFS data analysis in the RSXAP analysismore » package, and demonstrate its applicability with a few examples, including determining whether a particular scattering shell is warranted, and differentiating between two possible species or two possible structures in a given shell.« less
  • A general problem when fitting EXAFS data is determining whether particular parameters are statistically significant. The F-test is an excellent way of determining relevancy in EXAFS because it only relies on the ratio of the fit residual of two possible models, and therefore the data errors approximately cancel. Although this test is widely used in crystallography (there, it is often called a 'Hamilton test') and has been properly applied to EXAFS data in the past, it is very rarely applied in EXAFS analysis. We have implemented a variation of the F-test adapted for EXAFS data analysis in the RSXAP analysismore » package, and demonstrate its applicability with a few examples, including determining whether a particular scattering shell is warranted, and differentiating between two possible species or two possible structures in a given shell.« less
  • Purpose: Evaluate the ability of different dosimeters to correctly measure the dosimetric parameters percentage depth dose (PDD), tissue-maximum ratio (TMR), and off-axis ratio (OAR) in water for small fields. Methods: Monte Carlo (MC) simulations were used to estimate the variation of k{sub Q{sub c{sub l{sub i{sub n,Q{sub m{sub s{sub r}{sup f{sub c}{sub l}{sub i}{sub n},f{sub m}{sub s}{sub r}}}}}}}}} for several types of microdetectors as a function of depth and distance from the central axis for PDD, TMR, and OAR measurements. The variation of k{sub Q{sub c{sub l{sub i{sub n,Q{sub m{sub s{sub r}{sup f{sub c}{sub l}{sub i}{sub n},f{sub m}{sub s}{sub r}}}}}}}}}more » enables one to evaluate the ability of a detector to reproduce the PDD, TMR, and OAR in water and consequently determine whether it is necessary to apply correction factors. The correctness of the simulations was verified by assessing the ratios between the PDDs and OARs of 5- and 25-mm circular collimators used with a linear accelerator measured with two different types of dosimeters (the PTW 60012 diode and PTW PinPoint 31014 microchamber) and the PDDs and the OARs measured with the Exradin W1 plastic scintillator detector (PSD) and comparing those ratios with the corresponding ratios predicted by the MC simulations. Results: MC simulations reproduced results with acceptable accuracy compared to the experimental results; therefore, MC simulations can be used to successfully predict the behavior of different dosimeters in small fields. The Exradin W1 PSD was the only dosimeter that reproduced the PDDs, TMRs, and OARs in water with high accuracy. With the exception of the EDGE diode, the stereotactic diodes reproduced the PDDs and the TMRs in water with a systematic error of less than 2% at depths of up to 25 cm; however, they produced OAR values that were significantly different from those in water, especially in the tail region (lower than 20% in some cases). The microchambers could be used for PDD measurements for fields greater than those produced using a 10-mm collimator. However, with the detector stem parallel to the beam axis, the microchambers could be used for TMR measurements for all field sizes. The microchambers could not be used for OAR measurements for small fields. Conclusions: Compared with MC simulation, the Exradin W1 PSD can reproduce the PDDs, TMRs, and OARs in water with a high degree of accuracy; thus, the correction used for converting dose is very close to unity. The stereotactic diode is a viable alternative because it shows an acceptable systematic error in the measurement of PDDs and TMRs and a significant underestimation in only the tail region of the OAR measurements, where the dose is low and differences in dose may not be therapeutically meaningful.« less
  • Three topics already published by the H1 Collaboration are described: the gluon determination from a QCD fit to F{sub 2} data, the charm structure function and an extraction of F{sub L}.