2005 Unbinned Point Source Analysis Update

1
2005 Unbinned Point Source Analysis Update

• Jim Braun
• IceCube Fall 2006 Collaboration Meeting

2
Review -- Inefficiency of Binned Methods

• Unused information
• Event loss
• Distribution of events within bin
• Track resolution
• Event energy
• Optimization
• Bin sizes optimized to set the lowest flux limit
  are not optimal for 5s discovery
• Unbinned search methods should be better in every
  way
• Except work needed to implement them

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Review -- Methods

• Comparison of two likelihood approaches with
  standard binned approach
• Gaussian likelihood
• Assume signal distributed according to 2D
  gaussian determined from MC
• Paraboloid likelihood
• Space angle error estimated on event-by-event
  basis
• The signal uniform background hypothesis
  contains an unknown number of signal events out
  of Nband total events in declination band around
  source. Minimize -Log likelihood to find best
  number of signal events

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Review -- Methods

• Test hypothesis of no signal with likelihood
  ratio
• Compare likelihood ratio to distribution obtained
  in trials randomized in RA to compute
  significance
• Compare methods at fixed points in the sky
• Simulate signal point source events with neutrino
  MC in fixed declination bands
• Choose 1000 random background events from
  neutrino MC
• Apply 2005 filter and 2000-2004 point source
  quality cuts
• For binned search, optimize bin radius to
  minimize m90(Nbkgd)/Ns

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Detection Probability

• Gaussian and paraboloid methods perform similarly
• Paraboloid resolution quality cut applied to
  simulation, paraboloid method may improve with
  looser cut
• Clear 15-20 decrease in number of events needed
  to achieve a given significance and detection
  probability compared to binned method
• More to gain for hard spectra
• Use energy information in likelihood formulation

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What if there is no Signal?

• In the absence of signal, how do limits
  (sensitivity) of unbinned searches compare with
  binned?
• Sensitivity of binned searches
• Calculate Nbkgd for optimal search bin at
  selected zenith angles
• Look up m90(Nbkgd) from Feldman-Cousins Poisson
  tables
• Sensitivity m90(Nbkgd) F / Ns(F)
• Unbinned searches
• No Poisson Statistics
• No number of observed events
• Need to create analysis-specific Feldman-Cousins
  confidence tables

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Feldman-Cousins Tables

• Given an observation of observable o, we would
  like to place limits on some physical parameter m
• Past AMANDA point source searches
• Observable o number of events in the search bin
• Parameter m neutrino flux from a source in
  direction of search bin
• We can calculate P(om)
• For a search bin with N events and B expected
  background, P(om) is Poisson probability of N
  events given mean (m B)
• For each m, integrate probability until desired
  coverage is reached (typically 90)
• Order by P(om)/P(ombest) to determine which
  values of the observable are included in
  acceptance region
• This confidence belt in o-m space contains 90
  of total probability
• In 90 of observations of observable o, the true
  value of m will lie in the confidence belt.
• 90 upper and lower confidence limits given
  observable o correspond to confidence belt
  maximum and minimum values of m

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Feldman-Cousins Tables

• Construction of confidence belts for likelihood
  searches
• m Poisson mean number of true events,
  corresponding to flux
• o ANY observable
• Choose Tills significance estimate as the
  observable
• Need table of P(zm) on a fine grid of m
• Choose number of signal events (N) from Poisson
  distribution with mean m
• Calculate significance estimate and repeat 10k
  times
• Significance estimate distribution yields P(zm)

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Feldman-Cousins Tables

• Easier in practice
• Can simulate sources with Nt events and weight by
  Poisson probability of Nt for a given m

• Confidence belts constructed by integrating
  probability for each m to 90
• Average upper limit calculable using confidence
  band and z distribution for m 0

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Sensitivity Comparison

• Compare sensitivity of likelihood methods to
  sensitivity of binned cone search at three zenith
  angles
• 22-24 better sensitivity at d22.5o , similar
  to gain in detection probability
• Again, more to gain for hard spectra with energy
  information in likelihood function
• If Nch is cut parameter, then for E-2 fluxes
  limits should be better than with optimal Nch cut

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Roadmap to Unblinding

• Significant work yet to be done to unblind 2005!
• Addition of energy estimator to likelihood
  function
• May be as simple as Nch
• 2005 neutrino sample selection
• Cuts intended to maximize neutrino efficiency
• The future
• Analyze 2000-2005(6) (possibly 1997-2006)

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Questions/Comments