2005 Unbinned Point Source Analysis Update Jim Braun
2005 Unbinned Point Source Analysis Update Jim Braun IceCube Fall 2006 Collaboration Meeting Review -- Inefficiency of Binned Methods Unused information Event loss Distribution of events within bin Track resolution Event energy Nch = 20 Nch = 24 Nch = 26 Case 1: Nbin = 3 Optimization
Bin sizes optimized to set the lowest flux limit are not optimal for 5 discovery Unbinned search methods should be better in every way Except work needed to implement them IceCube Collaboration Meeting Fall 2006 Nch = 28 Nch = 60 Nch = 102 Case 2: Nbin = 3 2005 Unbinned Point Source Analysis Update: 2 Review -- Methods
Comparison of two likelihood approaches with standard binned approach Gaussian likelihood Paraboloid likelihood Assume signal distributed according to 2D gaussian determined from MC x1 Space angle error estimated on event-by-event basis x2 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 IceCube Collaboration Meeting Fall 2006
2005 Unbinned Point Source Analysis Update: 3 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 IceCube Collaboration Meeting Fall 2006 90(NNbkgd)/NNs 2005 Unbinned Point Source Analysis Update: 4 Detection Probability Detection Probability =22.5o =180o, 1000 Background Events
Gaussian and paraboloid methods perform similarly Likelihood 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 Binned (NCone) 3
5 IceCube Collaboration Meeting Fall 2006 Paraboloid resolution quality cut applied to simulation, paraboloid method may improve with looser cut Use energy information in likelihood formulation 2005 Unbinned Point Source Analysis Update: 5 What if there is no Signal? In the absence of signal, how do limits (Nsensitivity) of unbinned searches compare with binned? Sensitivity of binned searches: Calculate Nbkgd for optimal search bin at selected zenith angles Look up 90(NNbkgd) from Feldman-Cousins Poisson tables Sensitivity = 90(NNbkgd) * /N Ns(N) Unbinned searches
No Poisson Statistics No number of observed events Need to create analysis-specific Feldman-Cousins confidence tables IceCube Collaboration Meeting Fall 2006 2005 Unbinned Point Source Analysis Update: 6 Feldman-Cousins Tables Given an observation of observable o, we would like to place limits on some physical parameter Past AMANDA point source searches Observable o = number of events in the search bin Parameter = neutrino flux from a source in direction of search bin We can calculate P(No|)
For a search bin with N events and B expected background, P(No|) is Poisson probability of N events given mean (N + B) For each , integrate probability until desired coverage is reached (Ntypically 90%) Order by P(No|)/NP(No|best) to determine which values of the observable are included in acceptance region This confidence belt in o- space contains 90% of total probability In 90% of observations of observable o, the true value of will lie in the confidence belt. 90% upper and lower confidence limits given observable o correspond to confidence belt maximum and minimum values of IceCube Collaboration Meeting Fall 2006 2005 Unbinned Point Source Analysis Update: 7 Feldman-Cousins Tables Construction of confidence belts for likelihood searches = Poisson mean number of true events, corresponding to flux o = ANY observable Choose Tills significance estimate as the observable
Need table of P(N|) on a fine grid of Choose number of signal events (NN) from Poisson distribution with mean Calculate significance estimate and repeat ~10k times Significance estimate distribution yields P(N|) IceCube Collaboration Meeting Fall 2006 2005 Unbinned Point Source Analysis Update: 8 Feldman-Cousins Tables P(|) =22.5, 1000 Background Events Easier in practice: Can simulate sources with Nt events and weight by Poisson probability of Nt for a given FC 90% Conf. Band =22.5, 1000 Bkgd Events Confidence belts constructed by integrating probability for each to 90%
Average upper limit calculable using confidence band and distribution for = 0 IceCube Collaboration Meeting Fall 2006 2005 Unbinned Point Source Analysis Update: 9 Sensitivity Comparison Gaussian LH Paraboloid LH Compare sensitivity of likelihood methods to sensitivity of binned cone search at three zenith angles
22%-24% better sensitivity at =22.5o , similar to gain in detection probability Again, more to gain for hard spectra with energy information in likelihood function IceCube Collaboration Meeting Fall 2006 If Nch is cut parameter, then for E-2 fluxes limits should be better than with optimal Nch cut 2005 Unbinned Point Source Analysis Update: 10 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(N6) (Npossibly 1997-2006) IceCube Collaboration Meeting Fall 2006 2005 Unbinned Point Source Analysis Update: 11 Questions/Comments IceCube Collaboration Meeting Fall 2006 2005 Unbinned Point Source Analysis Update: 12
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