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Normalization, reweighting, and the scale factor:

  1. Jan 30, 2010 #1
    Hi all,

    I am about to begin my studies as an experimentalist and I keep hearing about these terms when someone represents his data as histograms.
    Can some one here, please, give me a clear explanation about their meanings.
    My background is theory and you can use as much mathematics as you can!

    Thanks a lot in advance,

    ~mborn
     
  2. jcsd
  3. Jan 30, 2010 #2
    normalization: generally this term comes in spectrum...after getting a experimental spectrum one often normalize it...experimental spectrum and normalized spectrum are same but with different y-axis value..for e.g., area of a exp. spectrum is different from normalized spectrum..usually a normalized one's area is often 1 or some value.
    reweighting..:similar to normalization..it depends on experiment.
    scale factor: usually multiplying either x- or y-axis by a constant.
    hope this help
     
  4. Jan 30, 2010 #3
    To make things eaiser, let's say you are in a a particle physics experiment that is trying to discover a particle.
    Now, for normalization, how can we make the area under the histogram equal one?
    Can you elaborate more on reweighting? What is the difference between reweighting (to Monte Carlo) and normalization?

    ~mborn
     
  5. Jan 30, 2010 #4
    Hi,
    normalization(actually this is a general technique used everywhere not only for particle physics):
    think..we have a exp. spectrum [tex]\int I(E)\;{\rm d}E=X[/tex]
    now we will normalize that spectrum such that area under the spectrum is 1.
    So what ppl. usually do is
    [tex]\int I_{\rm norm}(E)\;{\rm d}E=\frac{1}{X}\int I(E)\;{\rm d}E=1[/tex]
    This is how a normalization done.[but i am not completely sure..i assume others from this forum may correct us in case of error.]
    Now i can give a example for weighing (i dont know exactly what is reweighing?).
    in this integral:
    [tex]\int \frac {I(E)}{E}\;{\rm d}E[/tex]
    [tex]I(E)[/tex] is weighed by a factor of [tex](1/E)[/tex]
    hope it may help..
     
    Last edited: Jan 30, 2010
  6. Jan 31, 2010 #5
    Thank you Rajini,

    So, I am OK now with normalization! Still I hope someone here will explain reweighting for us.
    As far as I know, reweighting is to divide the number of events in each bin of a histogram by the total number of events. If this is true, then why do we need to do reweighting?

    ~mborn
     
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