From: Sébastien Gadrat <gadrat_at_clermont.in2p3.fr>

Date: Tue, 03 May 2005 01:45:43 +0200

Date: Tue, 03 May 2005 01:45:43 +0200

Hi rooters,

I am puzzling with the errors returned by a likelyhood fitting made in two different ways.

- First way, I plotted dimuon invariant mass data on a TH1 histogram with variable bining (first bins have width of 0.3 GeV then some with width equal to 0.6 and then a few with 0.9 GeV). I decided to normalize each bin by the size of the smallest bin (here is 0.3 GeV) so a bin represent the number of events per mass unit per 0.3 GeV. Then I apply my fit function (which is a sum of simple fits) on this histo by:

hSigFitbgd->Fit(myFitFunction,"ILLEM","",xlow,xhigh);

I use "LL" option to use log likelyhood minimisation for bin entries
which are not integers (as I read in the documentation).
I have three parameters in my fit function. I found for these three fit
the follwing :

First parameter : 489 ± 25

Second parameter : 154 ± 45

Third parameter : 270 ± 50

Comparing these numbers to a Chi square method fit results looks
reasonable except that I get smaller error especially for the second
parameter :

First parameter : 489 ± 30

Second parameter : 154 ± 89

Third parameter : 270 ± 57

Since the statistics is low I assume the error are smaller because log likelyhood is more suited for low statistics sample.

But now (second way of fitting), I just remove the normalisation by the
smallest bin so a bin entry just is the number of events per mass unit

*(delta N/delta M). Now I just apply the exactly same fit function and I *

get very small error like :

First parameter : 489 ± 11

Second parameter : 155 ± 22

Third parameter : 268 ± 26

The two ways are exactly the same except for the building of the
histogram to fit. It seems that the removal of the normalisation factor

*(actually the 0.3 normalisation factor) cause a impressive decrease of *

the error. I was wondering how the likelyhood method handle the error
propagation... Does anyone have an idea ?
Thanks in advance,

Sebastien

PS : I did not make a simple macro since I wonder whether this is a known problem and just a wrong use of the likelyhood method. I will make one if needed !! Received on Tue May 03 2005 - 01:45:50 MEST

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