Multivariate Discriminant Analysis applied to classification of ne CC events in MINOS Update

1
Multivariate Discriminant Analysisapplied to
classification of ne CC events in MINOS-Update-

• Alex Sousa
• Tufts University
• Tufts Harvard Brookhaven Meeting
• 09/01/2004

2
Changes since Ely

• New MDC sample fully reprocessed with R1.9.
• Consolidation of analysis framework
• Developed in C/ROOT, independent of Minossoft.
• Uses Sues ntuple format
• Includes Joshs Vertex Finder package
• Unsynced Reco and Truth trees Handling (corrected
  some bugs and increased algorithm speed and
  robustness)
• Easy reading of analysis variables with cuts and
  easy creation of oscillated samples
• Now has an Event Display
• CVS repository of the code available on the Tufts
  MINOS server.
• Identified and corrected problem leading to
  overestimation of NC and CC events from nt

3
MDA Procedure

• Define a set of variables that
  appropriately describes the data sample.
• Calculate the covariance matrix for each class
  
• Determine the Mahalanobis distance to each class
  for each event
• Compute the probabilities for an event to belong
  to each class (scores).

4
Samples

• Sample contents
• Constructed from 18 nm, 9 ne, and 39 nt MDC
  ntuples processed with release R1.9 in the batch
  farm and in the Tufts server.

5
Variable Selection

• Variable selection was performed using SAS
  Stepwise discriminant procedure
• Original 77 variables sorted by discriminant
  power
• All discrete variables removed
• Continuous variables sorted
• 29 variables selected for testing on the training
  sample
• Best results for 17 variables
• ph_pe
• uv_rms
• trk_ph_pe
• e_hit_total
• uv_asym_peak
• uv_kurt
• e_hit_trans_ratio

• trk_pe_ratio trk_ntrklike_ratio caldet_comp
• s_hit_trans chisq_ndf e_hit_long shwmax
• theta_hit_energy theta_hit_far e_hit_trans_long

6
Some Selected Variables
7
Probability Distributions
Training Sample
Training Sample

• Decide on an appropriate threshold by calculating
  the Figure of Merit for each threshold in the
  training sample.

8
Results (contd)
Test sample
Test sample
9
Event Display
non QE CC (DIS) event 1-y-0.861055 Enu4.742804
Elep-4.083814 emfrac0.862815
10
Event Display
Neutral Current event 1-y0.000000 Enu5.235544
Elep0.000000 emfrac0.443711
11
Event Display
non QE CC (DIS) event 1-y0.000000 Enu3.573198
Elep0.000000 emfrac0.632600
12
Conclusions

• Direct comparison with Ely results show
  improvements.
• Need to try different sets of cuts.
• Look at ambiguous events with Event Display and
  try to optimize the set of variables used.
• Explore discriminating potential of Cos q vs f
  plot.
• Working on code to determine 90 confidence limit
  on q13 by fitting the oscillated training P(ne)
  distributions to the combined test sample
  distribution.