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Re: Fitting scheme (part 2/2 for Martin) [message #2008 is a reply to message #2007] 
Wed, 02 June 2010 05:56 
killenberg Messages: 125 Registered: July 2005 Location: CERN 



rosem 
killenb  ... For instance one can use the distance calculated with the hit included in the track fit and multiply it by sqrt(n) / sqrt(nDoF), where n is the number if hits in the track and DoF is the number of degrees of freedom in the track fit.
 ...Do you have a reference where this is described or shown?

I use Wikipedia because it is easy to link.
For the 1D case of a Gaussian distribution there is only one free parameter, the mean of the distribution. In this case the factor is n1, known as Bessel's correction. The variance calculated using n1 is the sample variance.
For the 2D case of a linear regression (which is an ordinary least squares estimator) I use the German text book
Lothar Sachs, "Statistische Methoden", Springer Verlag 1979, ISBN 3540092269, chapter 8.6
In
Frederick James, "Statistical Methods in Experimental Physics, 2nd Edition", World Scientific 2006, ISBN 9812705279, chapter 8.4.1
I find that the method is retrieved for a linear function of the free parameters. (see also German Wikipedia page about linear regression. On the English page I could not find it).
I don't know how well a linear approximation is fulfilled for our helix fit.
However, the nDoF correction can be turned on in the BiasedResidualsProcessor and we can compare it to the geometric mean method. It uses DoF = 3 for a helix in the xy/rphi plane (2 for a straight line), and 2 in the sz plane.
Cheers
Martin
Martin Killenberg
CERN
martin.killenberg@cern.ch



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