Trying several fits with only 2 functions?

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Discussion Overview

The discussion revolves around the statistical methods used for fitting data in the context of a physics paper, specifically regarding the use of two fitting functions to extrapolate background contributions in high-energy physics experiments. Participants explore the implications of fitting ranges and the evaluation of uncertainty in the fitting process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how multiple fits can be performed using only two fitting functions, suggesting that varying the ranges for each function might be implied.
  • Another participant interprets the different fit ranges as varying the parameters of the fitting functions over specified intervals.
  • Concerns are raised about the evaluation of uncertainty using the RMS of all attempted fits, with a request for clarification on its statistical basis.
  • It is noted that even if fits are made over partially overlapping ranges, the evaluation of average and RMS values at specific points may still be valid.
  • A participant emphasizes that the correlation of fits does not focus on data fluctuations but rather on the sensitivity to the fitting method itself.
  • One participant expresses skepticism about the validity of the fitting approach based on their own sketch, indicating potential issues with determining errors from the fitting values.
  • Another participant asserts that if the fits appear problematic, there may be an error in the fitting process itself.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of fitting ranges and the evaluation of uncertainty, indicating that the discussion remains unresolved with multiple competing perspectives on the fitting methodology.

Contextual Notes

Limitations include potential misunderstandings of the fitting process, the dependence on the chosen fitting ranges, and the implications of correlation between fits on uncertainty evaluation.

ChrisVer
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Well I was reading this paper http://inspirehep.net/record/1409825
and came across this comment:
The simulated top quark and diboson samples as well as the data-driven background estimate are statistically limited at large $m_T$. Therefore the expected number of events is extrapolated into the high $m_T$ region using fits. Several fits are carried out, exploring various fit ranges as well as the two fit functions f(m_T) = e^{-a} m^b_T m_T^{c \log m_T} and f(m_T) = \frac{a}{(m_T + b)^{c}}. The fit with the best \chi^2 /\text{d.o. f.} is used as the extrapolated background contribution, with an uncertainty evaluated using the RMS of all attempted fits

My question is basically a statistical one... how can you make several fits using only 2 fitting functions?
Or do they mean something like fitting with func1 in some ranges [a,b] with a,b varying?
Also I do not understand well the uncertainty evaluation using the RMS of all attempted fits [how it works statistically].
 
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ChrisVer said:
Or do they mean something like fitting with func1 in some ranges [a,b] with a,b varying?
That's how I would interpret the different fit ranges they tested.
ChrisVer said:
Also I do not understand well the uncertainty evaluation using the RMS of all attempted fits [how it works statistically].
For a given m_T, you look at the average and RMS of all the values the different fits have at that point.
 
mfb said:
For a given m_T, you look at the average and RMS of all the values the different fits have at that point.

hmm... even if those fits were made over a partially common range? eg [200,300] and [250,400] ?
 
The fits are correlated, sure, but you are not studying the sensitivity to the data fluctuations here, only the sensitivity to the fit method.
 
well my problem mainly comes from such a sketch I did on the scratch (so sorry for the wriggles and so on)...
maxresdefault.jpg

Obviously trying to determine an error based on what values the f1 and f2 have in some ranges (at eg the blue's peak) can be problematic...especially if your best fit happens to be that of f1.
 
Last edited:
Well, if the fits look like that, you are doing something wrong.
 

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