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Papers published on the arXiv often mention the notion of Figure of Merit (FOM). Can you explain what a Figure of Merit is, how it is used and what are its relations to statistics?

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One of the earliest references to Figure of Merit (FOM) in statistics is:

H.G. Balian and N.W.Eddy. Figure-of-merit (FOM), an improved criterion over the normalize chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks. Nuclear Instruments and Methods, 145:389–395, 1977

The goodness of fit of the equation to the data is expressed by FOM which is defined as follows: $$ FOM = \frac{\sum_{i=1}^n|y_i^{expt}-y_i^{fit}|}{\sum_{i=1}^n|y_i^{expt}|},\space\space i = 1...n $$

where $y_i^{expt}$ is experimental data, $y_i^{fit}$ is fitted data, $n$ is a number of measurements.

FOM is quite extensively used in spectrography to fit the spectrum curves. Fitting spectra (optical, X-ray, gamma and so on) with the usual least square minimization is a quite subjective procedure: you need not only to fit but as well to analyze residuals, account for different spectra shapes, variations in experimental techniques or control noises. The authors feel (and practice shows) that FOM reduce this subjectivity and it is less influenced by experimental techniques and applications. Basically if $FOM < 0.025$ it's a good fit.

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