Trying several fits with only 2 functions?

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In summary: 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.
  • #1
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 [itex]f(m_T) = e^{-a} m^b_T m_T^{c \log m_T}[/itex] and [itex]f(m_T) = \frac{a}{(m_T + b)^{c}}[/itex]. The fit with the best [itex]\chi^2 /\text{d.o. f.}[/itex] 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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  • #2
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.
 
  • #3
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] ?
 
  • #4
The fits are correlated, sure, but you are not studying the sensitivity to the data fluctuations here, only the sensitivity to the fit method.
 
  • #5
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:
  • #6
Well, if the fits look like that, you are doing something wrong.
 

1. What is the purpose of trying several fits with only 2 functions?

The purpose of trying several fits with only 2 functions is to determine which combination of the two functions best describes the data. By trying different combinations and comparing the results, scientists can identify the most accurate and precise fit for their data.

2. How do you choose which functions to use for the fits?

The choice of functions depends on the type of data being analyzed and the underlying theory or hypothesis being tested. Scientists often use known mathematical models or equations that are relevant to their research to choose the functions for fitting the data.

3. Can using only 2 functions accurately represent complex data?

It depends on the complexity of the data and the functions being used. In some cases, two functions may be sufficient to accurately represent the data, while in others, more functions may be needed for a better fit. Scientists must carefully evaluate the results and consider the limitations of using only two functions.

4. Is it necessary to try multiple fits with only 2 functions?

Yes, trying multiple fits is necessary to determine the best fit for the data. It allows scientists to compare the results and choose the most accurate and precise fit. Simply using one fit may not accurately represent the data or may lead to misleading conclusions.

5. What are the advantages of using only 2 functions for fitting data?

Using only 2 functions allows for a simpler and more straightforward analysis of the data. It also helps to avoid overfitting, which can occur when too many functions are used to fit the data, leading to inaccurate results. Additionally, using fewer functions can save time and resources in the data analysis process.

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