Maximum-likelihood fits to histograms for improved parameter estimation
Abstract
Straightforward methods for adapting the familiar chi^2 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-alpha fluorescence spectrum, a poor choice of chi^2 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 chi^2 minimization. Where the modification is not possible, another approach allows iterative approximation of the maximum-likelihood fit.
Cite
@article{arxiv.1312.5622,
title = {Maximum-likelihood fits to histograms for improved parameter estimation},
author = {Joseph W. Fowler},
journal= {arXiv preprint arXiv:1312.5622},
year = {2014}
}
Comments
Accepted by J. Low Temperature Physics, in the Proceedings of Low Temperature Detectors 15