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Efficient maximum likelihood estimator fitting of histograms

Nature Methods volume 7, pages 338–339 (2010)Cite this article

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To the Editor:

Scientists commonly form histograms of counted events from their data, and extract parameters by fitting to a known model. Anytime a scientist counts photons, molecules, cells or data for individuals in histogram bins and fits that to a distribution, he or she is fitting an event-counting histogram. Here we aim to convince the scientific community to use the maximum likelihood estimator (MLE) for Poisson deviates when fitting event-counting histograms rather than the typically used least-squares measure. We describe how to use the MLE to fit data efficiently and robustly, and provide example code (Supplementary Software).

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Acknowledgements

This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.

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Authors and Affiliations

  1. Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California, USA

    Ted A Laurence & Brett A Chromy

Authors
  1. Ted A Laurence
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  2. Brett A Chromy
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Correspondence to Ted A Laurence.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Note (PDF 870 kb)

Supplementary Software

C code for Levenberg-Marquardt minimization of MLE. (ZIP 17 kb)

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Laurence, T., Chromy, B. Efficient maximum likelihood estimator fitting of histograms. Nat Methods 7, 338–339 (2010). https://doi.org/10.1038/nmeth0510-338

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