Re: TPC vertex error estimates and cut parameters

From: Bjorn H Samset (bjornhs@rcf.rhic.bnl.gov)
Date: Wed Sep 13 2000 - 04:21:04 EDT

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    On Tue, 12 Sep 2000, Michael Murray Tel 409 845 1411,FAX 1899, Home 823 
    3386 wrote:
    
    >     Dear Bjorn,
    >              I just read "Vertex-determination from TPM1". For the
    cluster
    > algorithm I think that a better estimate of the uncertainty of the
    vertex
    > is the error on the mean of the gaussian rather than the RMS.
    > Imagine that you have 2 events with the same set of tracks. However
    > the first event produces only 3 clusters per track while the second
    > produces 10 clusters per track. Both events should have the same RMS of 
    > the vertex histogram but the second event will have many more events and
    > so a much smaller uncertainty in the mean.
    >   For the tracking algorithm you use a cut of Chi**2<5. It seems to me
    > that this cut should depend on the number of degrees of freedom in
    > your fit. I think it would be better to use the confidence level. This
    > is a statistical measure of the likelyhood that a fit to a
    > distribution with gaussian errors and N degrees of freedom would have a
    given
    > Chi**2. There was a CERNLIB routine in FORTRAN whose syntax was
    > conf_level = PROB(Chi**2, N_Degrees_of_freedom)
    > I'm sure this must exist in ROOT.
    
    Hi, Michael - thanks for your comments. The reason I use the RMS,
    calculated "by hand" by using the sigma from the fit and then counting the
    number of entries within three deviations, is that from working with the
    ROOT gauss-fitter I know that this gives a good signal of when the peak is
    "well fitted". When it comes to estimatimating the actual uncertanty,
    though, I agree with you that the error on the mean would give a better
    value.
    For the TrackVertexModule, I have actually not changed anyting about the
    uncertainty-estimate since JH wrote it a long time ago. The reason is the
    same one i gave in the note - tracking in TPM1 has been a problem up until
    not long ago, so this module is less tested. A confidence-level seems to
    be a reasonable thing to use here, and I see that ROOT in it's
    TMath-object has at lest something resembling this.
    
    I'm going to a meeting in Bergen for a few days now, but I'll look into
    this when I get back :-)
    
    ------------------------------------------------
    Bjorn H. Samset
    Master-student in Heavy Ion physics
    Mob: +47 92 05 19 98  Office: +47 22 85 77 62  
    Adr: Kri 2A709 Sognsveien 218 0864 Oslo
    



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