strange behavior of likelyhood fitting errors

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