[Halld-physics] pull distributions

[Elliott Wolin]

Hi,

One mis-statement in my earlier note about true pulls. 

The 100% correlation between the two quantities in the numerator makes 
all the difference...it removes the influence of off-diagonal elements 
of the error matrix and makes the denominator a function of the 
difference between the squares of diagonal elements, not the sum.  See 
Frodesen et al. for details.

Sorry for the confusion.

				Sincerely,
					Elliott
 

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Elliott Wolin
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Matthew Shepherd wrote:
> Hi Curtis (and others who are interested),
>
> A few quick responses.
>
> Regarding the off-diagonal matrix elements, we have worked through this when we did pull studies to validate the our PWA fitter.  Even with a non-diagonal error matrix you will get a unit Gaussian pull distribution by constructing pulls from just the diagonal elements.  This sort of makes sense -- the diagonal elements alone tell you how far you need to move a particular variable to get a one standard deviation change.  The off diagonal elements tell you about simultaneous motions of more than one parameter.  You can make a rotation to diagonalize the error matrix and again, plot pull distributions in this rotated coordinate system and still get unit Gaussians.
>
> I think we should set the kinematic fit aside for now and verify that the error matrices alone for individual tracks are correct, as Simon is studying.  (I'm probably stating the obvious.)  If the error matrices for the tracks aren't right, then we can't expect anything out of the kinematic fit to be correct.  We know from the calorimetry work, that the kinematic fitter seems to behave well when supplied with a combination of photons and their proper error matrices.
>
> Alternatively, if Jake wanted to continue his studies with kinematic fitting, he could use a parametric simulation that smears the track parameters in cartesian coordinates and provides the corresponding (diagonal) error matrix with the Gaussian smearing variances.  This is then a properly formulated list of tracks and error matrices that would be a valid input to a kinematic fit.  (How well it represents the actual detector may be a different question.)
>
> -Matt
>
>
>
> On Oct 25, 2010, at 1:26 PM, Curtis A. Meyer wrote:
>
>   
>>    I also recall many years ago looking into what happens when the 
>> error matricies
>> are not diagonal. The denominator is defined only using the diagonal 
>> elements
>> of the covariance matrix, both for starting values and the fit values.
>>
>>    With regard for Simon's work, where he is looking at individual 
>> tracks, I am
>> not 100% sure how to apply this though. The error matrix is the result 
>> of the fit.
>> In Jake's work, it is clearer a we have the pull's from the tracking, 
>> and then the
>> improved pulls after the kinematic fit.
>>
>>    I have placed the chapter (6) on the portal as GlueX-doc-1635:
>>
>>    Other references include:
>>
>>    Eadie, W. T. et al., Statistical methods in experimental physics 
>> (North-Holland, Amsterdam, 1986).
>>
>>   V. Blobel, Least squares methods, p. I 27, in Bock, R. K. et al. 
>> (eds.), Formulae and methods
>>   in experimental data evaluation with emphasis on high energy physics. 
>> (European Phys. Soc.,
>>   1984)
>> curtis
>>
>> -- 
>> Prof. Curtis A. Meyer		Department of Physics
>> Phone:	(412) 268-2745		Carnegie Mellon University
>> Fax:	(412) 681-0648		Pittsburgh PA 15213-3890
>> cmeyer at ernest.phys.cmu.edu	http://www.curtismeyer.com/
>>
>>
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>
>
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