Event selection via calculation and selection of highest likelihood.
Eric Clinton
May 19, 2006
Weekly PrimEx meeting
Selecting events via Likelihood
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Definition of Likelihood for a given event:
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Use un­normalized Probability functions
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Likelihood will thus span from 0 to 1.
Selection of the “best” event out of many combinatorial possibilities.
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Prob(X @ xo )*Prob(Y @ yo)*Prob(A @ ao)*.....
Removes need for background subtraction of some processes.
This has been done before. See clas note 03­017.
What is likelihood of an event?
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Define and characterize a number of parameters to determine probability of an event.
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Tagger/HyCal timing.
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Very gaussian.
Pi0 invariant mass as a function of cluster pair type.
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Tung­tung, glass­glass, Tung­Glass, and Glass­Tung
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Elasticity as a function of cluster pair type.
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First of cluster pair has higher energy cluster. Mass and Elasticity distributions may not be perfectly gaussian.
Multiply parameter (un­normalized) probability distributions together—this is Likelihood.
Pi0 Mass probability distributions
Fit parameters p1, p2 and p3 are mean, sigma, and skewness of gaussian
Please excuse the bad label on the x­axis of the tungstate mass plot(left).
Right mass plot­­tungstate(T) has a higher cluster energy than glass(G).
Elasticity probability distributions
Likelihood function permutations
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A­­Gaus(Timing)*Gaus(pi0 Mass)*Gaus(Elasticity)
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B­­Gaus(Timing)*Gaus(pi0 Mass)*Skew(Elasticity)
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C­­Gaus(Timing)*Skew(pi0 Mass)*Skew(Elasticity)
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D­­Gaus(Timing)*Skew(pi0 Mass)*Gaus(Elasticity)
Run through the permutations
BIER method results...
Pi0 BIER Subtraction function
Pi0 Yields
Results and Conclusions
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Total # of Primakoff Pi0's. All radiator B, carbon.
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Using 2 skewed gaussians­­9850. –
All other permutations­­10050.
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Mean is not the maximum of the probability dist for skewed gaussian.
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Skewed gaus prob dist will select different events than a reg. gaus PD.
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Permutation C is thus most discriminating likelihood.
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Likelihood method is well understood and robust.
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Timing sideband cut superfluous.
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All timing background should be put at small likelihood since it should be very inelastic or off mass.
Combinatorial background eliminated.