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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|
|Pages:||pp. 414 - 420|
|Keywords:||Histogram fitting,energy resolution,maximum likelihood|
|DOI:||http://dx.doi.org/10.1007/s10909-014-1098-4 (Note: May link to a non-U.S. Government webpage)|
|PDF version:||Click here to retrieve PDF version of paper (428KB)|