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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 Go to previous messageGo to previous message
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(n-DoF), 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 n-1, known as Bessel's correction. The variance calculated using n-1 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 3-540-09226-9, chapter 8.6

In
Frederick James, "Statistical Methods in Experimental Physics, 2nd Edition", World Scientific 2006, ISBN 981-270-527-9, 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 n-DoF 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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