2005 Unbinned Point Source Analysis Update

1. 2005 Unbinned Point Source Analysis Update Jim Braun IceCube Fall 2006 Collaboration Meeting

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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)

9. 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

10. 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

11. 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)

12. Questions/Comments