A Concise Method for Storing and Communicating the Data Covariance Matrix

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The covariance matrix associated with experimental cross section or transmission data consists of several components. Statistical uncertainties on the measured quantity (counts) provide a diagonal contribution. Off-diagonal components arise from uncertainties on the parameters (such as normalization or background) that figure into the data reduction process; these are denoted systematic or common uncertainties, since they affect all data points. The full off-diagonal data covariance matrix (DCM) can be extremely large, since the size is the square of the number of data points. Fortunately, it is not necessary to explicitly calculate, store, or invert the DCM. Likewise, it is not necessary ... continued below

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Larson, Nancy M October 1, 2008.

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The covariance matrix associated with experimental cross section or transmission data consists of several components. Statistical uncertainties on the measured quantity (counts) provide a diagonal contribution. Off-diagonal components arise from uncertainties on the parameters (such as normalization or background) that figure into the data reduction process; these are denoted systematic or common uncertainties, since they affect all data points. The full off-diagonal data covariance matrix (DCM) can be extremely large, since the size is the square of the number of data points. Fortunately, it is not necessary to explicitly calculate, store, or invert the DCM. Likewise, it is not necessary to explicitly calculate, store, or use the inverse of the DCM. Instead, it is more efficient to accomplish the same results using only the various component matrices that appear in the definition of the DCM. Those component matrices are either diagonal or small (the number of data points times the number of data-reduction parameters); hence, this implicit data covariance method requires far less array storage and far fewer computations while producing more accurate results.

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  • Report No.: ORNL/TM-2008/104
  • Grant Number: DE-AC05-00OR22725
  • DOI: 10.2172/941045 | External Link
  • Office of Scientific & Technical Information Report Number: 941045
  • Archival Resource Key: ark:/67531/metadc898260

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  • October 1, 2008

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Oct. 31, 2016, 7:39 p.m.

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Larson, Nancy M. A Concise Method for Storing and Communicating the Data Covariance Matrix, report, October 1, 2008; [Tennessee]. (digital.library.unt.edu/ark:/67531/metadc898260/: accessed November 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.