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2005 Unbinned Point Source Analysis Update. Jim Braun IceCube Fall 2006 Collaboration Meeting. d. Nch = 20. Nch = 24. Nch = 26. a. Case 1: N bin = 3. d. Nch = 28. Nch = 60. Nch = 102. a. Case 2: N bin = 3. Review -- Inefficiency of Binned Methods. Unused information Event loss

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2005 unbinned point source analysis update

2005 Unbinned Point Source Analysis Update

Jim Braun

IceCube Fall 2006 Collaboration Meeting

review inefficiency of binned methods
d

Nch = 20

Nch = 24

Nch = 26

a

Case 1: Nbin = 3

d

Nch = 28

Nch = 60

Nch = 102

a

Case 2: Nbin = 3

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
review methods
x1

x2

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
review methods1
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
detection probability
Detection Probability d=22.5oa=180o, 1000 Background Events

Likelihood

Binned

(Cone)

5s

3s

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
what if there is no signal
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
feldman cousins tables
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(o|m)
    • For a search bin with N events and B expected background, P(o|m) 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(o|m)/P(o|mbest) 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
feldman cousins tables1
Feldman-Cousins Tables
  • Construction of confidence belts for likelihood searches
    • m = Poisson mean number of true events, corresponding to flux
    • o = ANY observable
      • Choose Till’s significance estimate as the observable
  • Need table of P(z|m) 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(z|m)
feldman cousins tables2
P(z|m) d=22.5, 1000 Background Events

FC 90% Conf. Band d=22.5, 1000 Bkgd Events

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 limitcalculable using confidence band and z distribution for m = 0
sensitivity comparison
Gaussian LH

Paraboloid LH

q

Sensitivity Comparison
  • Compare sensitivity of likelihood methods to sensitivity of binned cone search at three zenith angles
  • 22%-24% better sensitivity at d=22.5o , 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
roadmap to unblinding
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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