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

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

• Alex Sousa
• Tufts University
• Tufts DoE Review
• 10/20/2004

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Introduction

• One of the most relevant MINOS goals is to search
  for sub-dominant nm-gtne oscillations.
• MINOS can potentially improve the limit on q13
  set by CHOOZ.
• The Tufts HEP Group is a very active participant
  on the MINOS ne CC Analysis Group
• Apply a Multivariate Discriminant Analysis (MDA)
  method to ne CC classification in the current
  state-of-the-art MonteCarlo sample (MDC)
• Built a common analysis framework in
  collaboration with the Harvard MINOS group.

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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).
• Procedure implemented using the SAS package

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Analysis Framework Overview
MDC ntuples
Variables ntuple
Variable generation
Sample selection
Cuts
Computation of results
Event Display
MDA output
SAS Input format
Variable selection
MDA classification
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Samples

• Sample contents
• Constructed from 20 nm, 9 ne, and 39 nt MDC
  ntuples processed with release R1.9 in the
  Fermilab batch farm and in the Tufts server.
• Visible energy and track length cuts optimized
  through use of decision trees.
• Mild containment cut eliminates background from
  nm events truncated at the end of the detector
• Training Sample

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Samples

• Test Sample

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Variable Selection

• Variable selection is performed using SAS
  Stepwise discriminant procedure
• Original 77 variables sorted by discriminant
  power
• 45 variables selected for running on the training
  sample
• Best results for 18 variables
• uv_rms
• plane_n
• ph_pe
• nstrip
• uv_kurt
• trk_plane_ntrklike
• e_hit_total
• ntrack
• s_hit_trans_ratio
• shw_nstrip_ratio

• trk_pe_ratio shw_ph_nstrip max_pe_plane chisq_ndf
• uv_asym_peak e_hit_long e_hit_trans
  trk_chi2_ndof

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Some Selected Variables
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MDA output (Probability Distributions)
Training Sample
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Threshold Determination

• Calculate the training sample Figure Of Merit for
  several possible thresholds. Apply threshold
  corresponding to highest FOM to test sample
  classification.

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Results (Energy Distributions )
Test Sample (no threshold)
NC
ne
Signal
BG
BG
nm
nt
BG
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Results (Energy Distributions )
Test Sample (T0.92)
ne
NC
nm
nt
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Results (Efficiencies )
Test Sample (T0.92)
NC
ne
nt
nm
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Results (ne appearance signal)
Test Sample (T0.92)
SignalBG
BG
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Results (comparison table)
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Comparison with other analyses
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Some events
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Some events
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Some events
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Current and Future Work

• Investigate clustering and discriminating power
  of
• cosq vs f distributions
• Understand backgrounds from short nm events and
  improve their rejection
• Perform thorough eye scanning of problem event
  samples to try to improve the discriminating
  variables
• Apply method to the Near Detector MDC files and
  extrapolate to Far to estimate the beam ne
  background
• Update numi-714 sensitivity and discovery contour
  plots.