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Re: Fitting scheme (part 2/2 for Martin) [message #2007 is a reply to message #1990] 
Wed, 02 June 2010 02:47 
rosemann Messages: 41 Registered: March 2009 Location: hamburg.de 



Hi Martin and Jason,
now come the "oops" parts.
killenberg  [...]rosemann 
residual  the geometrical distance in x/phi at constant y/r between an associated hit (from track finding) to its fitted track, when it is excluded from the fit distance  the geometrical distance in x/phi at constant y/r between an associated hit (from track finding) to its fitted track, when it is included from the fit
The resolution is then the geometric mean of both values. (For reference check e.g. Ralf Dieners thesis or physics/0402054)


Wrong on my part, the (generic) distance is not at a fixed value, but really the perpendicular distance. While I personally think that this is a small nightmare in reading the formulas (e.g. think about: polar coordinates for the hits and a helix), it needs to be written only once.
It seems that I had completely misunderstood something; I believed that the definition of resolution was like I stated in the previous post (taken at fixed row position)  but it turns out, that there was no such agreement and the actual use (also at DESY) is the perpendicular definition.
I'm still looking, if there ever was a common agreement about this definition; maybe even written down. Otherwise we should somehow specify this (but where?).
killenberg  [...]The geometric mean is used because it is an unbiased estimator for the resolution. But we always used the mean of the withs of the two distributions (with and without the specific hit used in the fit). I don't know which is correct, probably both methods are equivalent if you calculate it through.

I'm not sure if I can follow you here. Afaik the geometric mean method is the one described in the paper I mentioned before (physics/0402054).
killenberg  However, there are other methods to calculate an unbiased estimator. 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.

I've never seen this way of defining the resolution. This would be a nice way to determine it without needing to refit the track n1 times for n hits on the track. Do you have a reference where this is described or shown?
killenberg  Another method is to use an unbiased track estimate, for instance from a separate measurement with a hodoscope. Or using MC truth in simulation.

Agreed, but both are academic for the time being. But maybe still this year we will have something like a hodoscope for the LP...(?)
killenberg  [skip the longer part of the description]
I admit the scheme is complicated and a bit tangled, but I could not come up with a simpler solution for the functionality I wanted.[...]

I have thought a lot about the scheme and it seems to me that either way it will be some kind of conflict. What I'm doing right now is sort of "start all over" and see where I'm going. The base class is a good idea and I will build on it.
I definitely propose to discuss this in the next MarlinTPC meeting. Maybe I will come to the same conclusion as Martin. Maybe there are other solutions.
I will report my thoughts and findings also here, to allow other thoughts into to process.
Cheers,
Christoph
When you have eliminated the impossible, whatever remains, however improbable, must be the truth. (Sir A.C. Doyle in Sign of Four)



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