Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

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The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimates … continued below

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17 p.

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Stoneking, M. R. & Den Hartog, D. J. June 1996.

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The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimates for the fit parameters. They compare this method with a {chi}{sup 2}-minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than {approximately}20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers.

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17 p.

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INIS; OSTI as DE96012000

Medium: P; Size: 17 p.

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  • 11. annual high-temperature plasma diagnostics conference, Monterey, CA (United States), 12-16 May 1996

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  • Other: DE96012000
  • Report No.: DOE/ER/53198--274
  • Report No.: CONF-960543--26
  • Grant Number: FG02-85ER53198
  • Office of Scientific & Technical Information Report Number: 266730
  • Archival Resource Key: ark:/67531/metadc671902

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Office of Scientific & Technical Information Technical Reports

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Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • June 1996

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  • June 29, 2015, 9:42 p.m.

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  • April 7, 2017, 3:54 p.m.

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Stoneking, M. R. & Den Hartog, D. J. Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties, article, June 1996; United States. (https://digital.library.unt.edu/ark:/67531/metadc671902/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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