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MARS Stuff
Curtis Lansdell
University of Maryland
January 21, 2005
Milagro Collaboration Meeting
Outline
“Standard” Discrimination
MARS, Neural Networks, and x2
MARS Distributions and Q-factors
MARS and the Crab
GEANT 4
Eyeball Discrimination
p
x2

proton
gamma
AS+ORCOM
Old way to differentiate – x2 parameter
x2  nb2/mxPE
x2 > 2.5 yields Q ~ 1.7 using just AS layer (and ORCOM)
Retains 51%  and 8.5% hadron using 50 PMT trigger
R. Atkins et al., ApJ 595, 803 (2003).
Some Checks on MARS
Neural Networks, MARS should get the same or higher
Q-factors than x2
– ANN (run by Xianwu) and ROOT NN package had problems
recreating Q-factor from single variable (x2)
– ANN and ROOT NN also had problems getting Q-factors as high
as MARS for multiple variables.
– MARS gives Qs closer to x2
ROOT NN
MARS
Multilayer+Gaussian Fitters
MARS1 (Multivariate Adaptive Regression Splines)
– Should be able to determine the best parameters
– Provides probability of being signal: ln[P()/P(p)]
More positive means more -like
on-pond
off-pond
Relative Variable Importance
not in Crab REC data
core
x2
mxPE
∑PEt
∑PEb
∑PEo
nb2
nb8
par2d
hitas
hitmu
hitor
pchi2
grPEt
grPEb
latPEt
latPEb
On
41.73
2.565
0.000
0.000
6.839
0.000
3.604
45.06
61.66
0.000
100.0
39.18
0.000
0.000
58.07
44.48
Off
100.0
79.26
98.24
0.000
7.771
78.36
80.37
6.599
51.88
0.000
4.483
66.52
8.074
0.000
71.71
0.000
All
25.58
0.000
0.000
0.000
79.62
0.000
12.71
11.86
67.88
5.077
3.063
59.24
0.000
0.000
100.0
7.680
1J.
Friedman, “Multivariate Adaptive Regression Splines”, Annals of Statistics 19 (1991).
16 par model
Event Efficiencies
on-pond
off-pond
12 par model (for Crab)
on-pond
off-pond
Crab Results
Elapsed time = 416 days
Bin size = 1.3°
nAS > 55, nFit > 80 (multi-layer fits)
MARS used 12 par model (dAngle < 0.7 for gammas)
No extra cuts
x2
MARS (on=1, off=2.5)
MARS (1, 0.6)
MARS (0.8, 0.8)
Significance
2.65
4.56
2.66
3.62
3.27
On Source
2212841
240608
24681
69100
61763
Off Source
2208997.25
238434.3
24275.41
68177.84
60973.69
Excess
3843.75
2173.7
405.59
922.16
789.31
GEANT 4
Energies from 30 GeV to 100 TeV
Thrown out to 1 km and flat in radius
~70 M proton events created so far
– 4.4 k events trigger with nFit > 80 (7.8 k for nFit > 5)
Distributions still don’t match data well
– Even with correct quantum efficiencies
Continuing Onward…
MARS in conjunction with multilayer fitter appears to
result in better discrimination in MC events.
– Compared with neural network
Used ROOT NN package, but saw worse discrimination – maybe
more tuning of hidden layers/nodes will help
– Used 12 parameter MARS value cuts on Crab data
Worse significance than x2 > 2.5 (nFit > 80, multi-layer fits)
Oops, forgot to do energy weighting (used 2.4)
GEANT 4 events being produced
– A few strange numbers need to be examined from the output
– Will check more MC-data agreement
– Run MARS with new MC!
Need more proton triggers and start creating gamma events