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Publication Citation: Maximum-likelihood fits to histograms for improved parameter estimation

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Author(s): Joseph W. Fowler;
Title: Maximum-likelihood fits to histograms for improved parameter estimation
Published: February 07, 2014
Abstract: Straightforward methods for adapting the familiar χ2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the total number of events is large. For the case of estimating a microcalorimeter's energy resolution at 6 keV from the observed shape of the Mn K α fluorescence spectrum, a poor choice of χ2 can lead to biases of at least 10% in the estimated resolution when up to thousands of photons are observed. The best remedy is a Poisson maximum-likelihood fit, through a simple modification of the standard Levenberg-Marquardt algorithm for χ2 minimization. Where the modification is not possible, another approach allows iterative approximation of the maximum-likelihood fit.
Citation: Journal of Low Temperature Physics
Volume: 176
Issue: 3-4
Pages: pp. 414 - 420
Keywords: Histogram fitting,energy resolution,maximum likelihood
Research Areas: Statistics
DOI: http://dx.doi.org/10.1007/s10909-014-1098-4  (Note: May link to a non-U.S. Government webpage)
PDF version: PDF Document Click here to retrieve PDF version of paper (428KB)