Maximum-likelihood fits to histograms for improved parameter estimation

Published

February 7, 2014

Author(s)

Joseph W. Fowler

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

Download Paper

https://doi.org/10.1007/s10909-014-1098-4

Keywords

Histogram fitting, energy resolution, maximum likelihood

Citation

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 January 14, 2026)