1. 1 Glen Cowan Statistics Forum News Glen Cowan Eilam Gross ATLAS Statistics Forum CERN, 3 December, 2008

2. 2 Glen Cowan Statistics Forum News Higgs Combination Exercise  CSC note HG11 completed Statistics Book  Statistics FAQ Interactions with physics groups ATLAS/CMS Joint Statistics Meetings Recent Statistics Forum activity

3. 3 Glen Cowan Statistics Forum News Higgs combination complete (p 1473 of CSC book) Describes statistical methods for combination of search channels. Applies combination to (a subset of) Higgs channels: WW→e  (0-jet and 2-jet), , ,  ZZ(*)→4l Treats systematics by means of profile likelihood method. Considers fixed-mass hypothesis; look-elsewhere-effect must be studied separately. NB H   and WW CSC notes describe floating-mass fits. Some approximations used for discovery/exclusion significance. Valid for L > 2 fb . For lower L need toy MC methods. Does not represent final word on methods -- other developments ongoing (Bayesian, CLs, look-elsewhere-effect,...)

4. 4 Glen Cowan Statistics Forum News CSC HG11 People Editors: Eilam Gross, Glen Cowan Contacts for individual channels: WWBill Quayle  Yaquan Fang  Kyle Cranmer 4lAndrea Di Simone Note referee:Fabiola Gianotti Chapter referees:Fabio Cerutti, Bruno Mansoulie Chapter editors:Rachid Mazini, Bill Murray + e.g. Louis Fayard, Aleandro Nisati, Karl Jakobs, Dave Charlton, Ofer Vitells...

5. 5 Glen Cowan Statistics Forum News Reminder of combination method  represents all nuisance parameters, e.g., background rate, shapes  =1 is SM.  =0 is background only. The single-channel likelihood function uses Poisson model for events in signal and control histograms: There is a likelihood L i ( ,  i ) for each channel, i = 1, …, N. The full likelihood function is

6. 6 Glen Cowan Statistics Forum News Profile likelihood ratio To test hypothesized value of , construct profile likelihood ratio: Maximized L for given  Maximized L Equivalently use q  =  2 ln (  ): data agree well with hypothesized  → q  small data disagree with hypothesized  → q  large

7. 7 Glen Cowan Statistics Forum News p-value / significance of hypothesized  Test hypothesized  by giving p-value, probability to see data with ≤ compatibility with  compared to data observed: Equivalently use significance:

8. 8 Glen Cowan Statistics Forum News Sampling distribution of q  To compute p-value of hypothesized , need distribution f (q  |  ). For 5  discovery we need a p-value of 2.8 × 10  ; To estimate this using MC needs > 10 8 events. Wilk’s theorem: in large sample limit f (q  |  ) should approach with w = ½. (a “half-chi-square” distribution). Validation exercise shows approximation OK for L ≥ 2 fb . We use the half-chi-square approximation in the current note; for lower luminosities we will need MC to get f (q  |  ) (feasible for exclusion limits at 95% CL).

9. 9 Glen Cowan Statistics Forum News Example from validation exercise: ZZ (*) → 4l 5  level (One minus) cumulative distributions. Band gives 68% CL limits. ½2½2 ½2½2 ½2½2 ½2½2 Distributions of q 0 for 2, 10 fb  from MC compared to ½  2

10. 10 Glen Cowan Statistics Forum News Sensitivity Discovery: Generate data under s+b (  = 1) hypothesis; Test hypothesis  = 0 → p-value → Z. Exclusion: Generate data under background-only (  = 0) hypothesis; Test hypothesis . If  = 1 has p-value < 0.05 exclude m H at 95% CL. Estimate median significance by setting data equal to expectation values (Asimov data) or by using MC. For median, can combine significances of individual channels. For significance of e.g. a real data set, need global fit.

11. 11 Glen Cowan Statistics Forum News Combined discovery sensitivity 5s5s

12. 12 Glen Cowan Statistics Forum News Combined discovery sensitivity vs. m H, L Approximations not reliable below 2 fb -1 (usually conservative)

13. 13 Glen Cowan Statistics Forum News p-value of SM hypothesis ( m =1) vs. m H m H > 115 at 95% CL with 2 fb -1

14. 14 Glen Cowan Statistics Forum News Combined exclusion sensitivity vs. m H, L Approximations not reliable below 2 fb -1 (usually conservative)

15. 15 Glen Cowan Statistics Forum News Summary of the Higgs Combination Final draft on http://indico.cern.ch/conferenceDisplay.py?confId=25831 higgs_combo_csc_28nov08.pdf CSC book imminent, we are provisionally pages 1473 to 1516 Many issues/problems identified and worked through  useful. Only subset of methods explored  much more work left. Method now documented, global fit tools under development. We need to learn how to do this more quickly...

16. 16 Glen Cowan Statistics Forum News Statistics Forum Website: FAQ Some general items: PDG Chapters, Pedestrian's guide, Glossary,...

17. 17 Glen Cowan Statistics Forum News Statistics Forum FAQ  Notes This is a living document

18. 18 Glen Cowan Statistics Forum News Statistics Forum FAQ  Notes The “FAQ” consists of a collection of notes on specific questions use cases, examples,... Bayesian methods for ATLAS Higgs search (GC) Comparison of significance from profile and integrated likelihoods (GC, EG) Discovery significance with statistical uncertainty in the background estimate (EG, OV, GC) Error analysis for efficiency (GC) How to measure efficiency (DC) MC statistical errors in ML fits (GC) Covariance matrix for histogram made using seed events (GC) If you have a note which you think should be included here, or if you are interested to write such a note or comment on a note or request a note on a specific subject please let us know.

19. 19 Glen Cowan Statistics Forum News Interaction with physics groups Over past year much interaction with Higgs group  Combination exercise (relevant to other searches as well...) Continue to extend this to other groups (Exotics, SUSY, B-Physics,...) E.g. SUSY Group (Dan T.) posed several question which we have tried to answer in notes (see FAQ – Profile vs integrated likelihoods, correlations in histograms arising from resampling). Encourage talks from physics groups in Statistics Forum, e.g., Exotics Lepton+X (Luis F., 24.9.08) – discussions ongoing SUSY (Sascha C., today) B-Physics (Emmerich K., 28.7.08) – ongoing Will push for further interaction – written note is preferred outcome.

20. 20 Glen Cowan Statistics Forum News Joint ATLAS/CMS Statistics Forum Summer 08: agree to develop RooStats as common framework. Keep eye on ability to carry out independent validation. Key players: Kyle Cranmer (ATLAS) Gregory Schott (CMS) Wouter Verkerke (RooFit) Lorenzo Moneta (Root) Ongoing discussions on methodology Ideal is to use several methods (profile likelihood, Bayesian, Cls,...) for each result. Meetings: 25 September 2008 29 July 2008 4 September 2007 17 July 2007

21. 21 Glen Cowan Statistics Forum News Summary Higgs combination exercise complete Valuable exercise especially for developing profile likelihood Time to move on Encourage interaction with all physics groups ATLAS/CMS interaction focused on RooStats (  Kyle talk next)