1 Comparing Unbinned likelihood methods IceCube/Antares Common Point source analysis from IC22 & Antares 2007/2008 data sets J. Brunner

2 Likelihood definitions so far : no energy, global PSF ANTARES: S+B likelihood ANTARES: S+B likelihood IceCube: S+B likelihood IceCube: S+B likelihood signal PDF Signal events Poisson mean PSF Position in sky Background rate Total event n s =  sig F = S i

3 Normalization and differences Int 4 (F)=1 Int 4 (F)=1 Int 4 (B i )=N tot Int 4 (B i )=N tot N tot =Total number of observed events in full sky N tot =Total number of observed events in full sky Signal events are added on top of N tot Signal events are added on top of N tot Int 5º (S i )=1 Int 5º (S i )=1 Int 5º (B i )=1 (B i = cons) Int 5º (B i )=1 (B i = cons) N = total number of observed events inside search window N = total number of observed events inside search window Signal events are a fraction of N Signal events are a fraction of N Important to distinguish Integral over full sky versus Integral over Vicinity of source to build likelihood (here 5 degrees)

4 Combining Samples (Antares method) Add sum of j samples Add sum of j samples Each event knows from which sample it comes (indices ij) Each event knows from which sample it comes (indices ij) Each sample has its own background PDF B j Each sample has its own background PDF B j Each sample has its own PSF ß j Each sample has its own PSF ß j But only one  sig can be fitted But only one  sig can be fitted Relative contributions of samples to signal controlled by r j for each  Relative contributions of samples to signal controlled by r j for each 

5 Combining Samples (IceCube method) N : total number of events form all samples within search cone N : total number of events form all samples within search cone One PSF per sample One PSF per sample B j might still be constant for small search cones B j might still be constant for small search cones Relative contributions of samples to signal controlled by r j for each  Relative contributions of samples to signal controlled by r j for each 

6 Signal events Unified in bins of 10 degrees Unified in bins of 10 degrees Event per declination per reference flux Event per declination per reference flux Used for signal simulation and r j calculation Used for signal simulation and r j calculation ANT07 ANT08 IC22-UHE IC22 ALL

7 Signal events Fraction of events per declination band Fraction of events per declination band Northern hemisphere: IC22 contributes more than 95% Northern hemisphere: IC22 contributes more than 95% DEC<-50º: only ANTARES DEC<-50º: only ANTARES -50º -0º: ok -50º -0º: ok ANT07 ANT08 IC22-UHE IC22 Declination range where both experiments contribute more than 10% Chance to get events from both samples close to source

8 Code development Signal histos Background histos PSF histos Test experiments Fit within 5º from source Filenames NEXP Nsig Ra,Dec Command line Small root files Root Tree TS,LH(S+B),LH(B),sig SensitivityDiscovery powerFlux limits Root executable No graphics Runs in batch mode Small Root Macros Graphics output Interactive

9 Code development Everything is based on Root Everything is based on Root No dependence on heavy software packages like IceTray, SeaTray No dependence on heavy software packages like IceTray, SeaTray No dependence on custom formats like i3 No dependence on custom formats like i3 Test experiment drawing and LH fit coupled Test experiment drawing and LH fit coupled Restrict to 5º area around source for speed reasons Restrict to 5º area around source for speed reasons Heaviest part standalone executable Heaviest part standalone executable Mass production on batch farm at CC-LyonMass production on batch farm at CC-Lyon 18 declinations (-85º to 85º) in steps of 10º18 declinations (-85º to 85º) in steps of 10º Fixed (random) rectascensionFixed (random) rectascension Signal events from 0-29 : Total 540 jobs per roundSignal events from 0-29 : Total 540 jobs per round 10 7 TE for BG-only case, 10 6 otherwise10 7 TE for BG-only case, 10 6 otherwise

10 Example sky maps Point source with 20 events included Point source with 20 events included Rectascension Declinationion IC22 IC22-UHE ANT-2007 ANT2008

11 Example sky maps Point source with 20 events included Point source with 20 events included Rectascension Declinationion IC22 IC22-UHE ANT-2007 ANT2008

12 Example sky maps Point source with 20 events included Point source with 20 events included Reasonable mixture of both sets Reasonable mixture of both sets Rectascension Declinationion IC22 IC22-UHE ANT-2007 ANT2008

13 Example of Teststatistics 10 signal events added 10 signal events added Comparison of IceCube Antares LH ratio Comparison of IceCube Antares LH ratio Slight differences Slight differences Both too low in this example Both too low in this example

14 Examples for TestStatistics Antares method Antares method More pronounced change in TS in Southern hemisphere More pronounced change in TS in Southern hemisphere Less Background Less Background signal events DEC=-35º DEC=+35º

15 Examples for TestStatistics DEC=-35º More pronounced change in TS of Antares More pronounced change in TS of Antares signal events ANTARESIceCube

16 Examples for Fitted Nsig ANTARES method Antares region (South) Antares region (South) fitted values are systematic 8% lowfitted values are systematic 8% low Effect of 5º cutoff in PSF for fitEffect of 5º cutoff in PSF for fit IceCube IceCube Fitted values ok within 2%Fitted values ok within 2% Effect ignored in the following Effect ignored in the following signal events DEC=-35º DEC=+35º fitted fitted

17 Examples for Fitted Nsig On average compatible fit results On average compatible fit results Strange pattern in IceCube fit Strange pattern in IceCube fit Disappears for higher statistics (Northern hemisphere) Disappears for higher statistics (Northern hemisphere) signal events ANTARES fitted fitted IceCube

18 Discovery power Cumulative TS distribution for BG-only experiments Cumulative TS distribution for BG-only experiments Exponential fit Exponential fit Retain 3, 5 TS values from single-sided Gaussian ( , ) Retain 3, 5 TS values from single-sided Gaussian ( , ) DEC=-35º DEC=+35º

19 Discovery power Typical quote of discovery power: 50% chance to have a 3, 5 effect Typical quote of discovery power: 50% chance to have a 3, 5 effect DEC=-35º Single source DEC=-35º 24 sources approximation DEC=+35º 24 sources approximation

20 Results : Discovery power Declination dependence over full sky Declination dependence over full sky Trial factor for 24 sources included in approximate way Trial factor for 24 sources included in approximate way 3 53 5 3 53 5 Event numbers Neutrino Flux

21 Comparison of limit setting methods DEC=+35º Neyman Median=3.8 DEC=-35º Neyman Median=2.7 DEC=+35º CLs method Median=5.8 DEC=-35º CLs method Median=3.8 DEC=-70º Antares Neyman 2.0 F&C 2.4 CLs 2.8

22 Comparison of limit setting methods DEC=+35º Neyman Median=3.8 ANTARES DEC=+35º Neyman Median=4.3 IceCube DEC=+35º CLs method Median=5.8 ANTARES DEC=+35º CLs method Median=6.9 IceCube DEC=-70º Antares Neyman 2.0 F&C 2.4 CLs 2.8

23 Sensitivities in comparison ANTARESIceCube Sensitivity is average of actual limit points 50% of points above, 50% below Sensitivity coincides with best limits i.e. those which are most BG-like Not entirely understood: Difference in likelihood definition Difference in treatment of TS=0 peak for bg-only test experiments

24 Results : Sensitiviy - Flux Reproduce Antares & IC22 where one experiment dominates Reproduce Antares & IC22 where one experiment dominates Coherent limit for whole sky Coherent limit for whole sky 90% C.L. Neyman CLs IC22 IC22-UHE Antares

25 Next steps Further comparison of both methods Further comparison of both methods Understand differences in limit fluctuations Understand differences in limit fluctuations Further steps in combined analysis Further steps in combined analysis Understand differences in differential sensitivities Understand differences in differential sensitivities

Chad Finley26 Differential sensitivity ? Still open problem ANTARES ? MANTS 2009 : Chad Finley