1. Project on H→ττ and multivariate methods
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2. Motivations
Define a multivariate classifier to separate signal from background;
Improve the procedure that produces the selection region based on the classifier and determine the expected discovery significance ;
Extend the analysis to multiple bins to make significant improvements possible.
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3. Strategies
Fisher
BDT
MLP
Binned Analysis
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4. Fisher
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5. Fisher
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6. BDT
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7. BDT
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8. MLP

9. Analysis
Binned analysis: Choose some number of bins (~40) for the histogram of the test statistic. In bin i, find the expected numbers of signal or background:
Likelihood function for strength parameter μ with data n1,..., nN:
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10. Analysis show that ln L(μ) can be written:
where C represents terms that do not depend on μ.
Therefore, to find the estimator μ, we solve:
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11. Analysis Statistic for test of μ = 0:
Estimate the discovery significance (significance of test of μ= 0) from the formula:
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12. Analysis
Overlook the unimportant information from each event’s value of the statistic t :
DER prodeta jet jet : The product of the pseudorapidities of the two jets (undefined if PRI jet num ≤ 1).
DER lep eta centrality : The centrality of the pseudorapidity of the lepton with regard to the two jets.
PRI jet leading phi : The azimuth angle f of the leading jet (undefined if PRI jet num = 0).
PRI jet subleading pt : The transverse momentum of the leading jet, that is, the jet with second largest transverse momentum (undefined if PRI jet ≤ num 1).
PRI jet subleading eta : The pseudorapidity h of the subleading jet (undefined if PRI jet num ≤ 1).
PRI jet subleading phi The azimuth angle f of the subleading jet (undefined if PRI jet num ≤ 1).
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13. Conclusions
Optimize the value of tcut to obtain the maximum expected discovery significance.
Fisher . tcut= 0.2 ; Z0= ; ZA =
BDT . Tcut = 0.3 ; Z0= ; ZA=
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14. Conclusions
Use the routine fitPar.cc to solve the equation .Then we find μ hat = 1 and use the Asimov data set to evaluate q0 and use this with the formula Z = √q0 to estimate the median discovery significance.
Fisher : q0 =
Z =
BDT ： q0 =
Z =
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15. Outlook Binned analysis : numbers , weights.
GPU Parallel Computing to improve efficiency.
Stimulated data from experiment.
SVM, generate ni ~ Poisson(bi) to search for p-value to estimate the discovery significance.
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16. THANKS!
Zheng Yi
Xu Hongge
Li Ruibo
Ding Wei
Hu Boshen
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