Fowler, J.
(2014),
Maximum-likelihood fits to histograms for improved parameter estimation, Journal of Low Temperature Physics, [online], https://doi.org/10.1007/s10909-014-1098-4
(Accessed May 2, 2025)
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Maximum-likelihood fits to histograms for improved parameter estimation
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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
Pub Type
Journals
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Keywords
Histogram fitting, energy resolution, maximum likelihood
Citation
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Created February 7, 2014, Updated November 10, 2018