1. 1 Summary and Conclusions Kyle Cranmer (New York University) Harrison B. Prosper (Florida State University) Sezen Sekmen (CERN) LPCC Workshop: Likelihoods for LHC Searches LPCC Workshop on Likelihoods CERN

2. List of Talks Day 1  SezenGoals  GlenPrinciples  KyleContext/Scope Feedback  Marco  Maggie  Béranger Day 2  KyleHistFactory  SvenATLAS HZZ4l Higgs Combination  MinshuiCMS  HaoshuangATLAS Day 3  Wolfgang  Javier (thanks Maurizio!)  Wouter Panelists Sünje, Mike, Lorenzo 2LPCC Workshop on Likelihoods CERN

3. DAY 1 LPCC Workshop on Likelihoods CERN3

4. Sezen: Workshop Goals Goals  Educate ourselves: why are likelihoods needed?  Move towards routine publication of likelihoods LPCC Workshop on Likelihoods CERN4

5. Glen: Basic Ideas Distribution Probability density (or mass) function, Nature(x) xpotential observations Model P(x | μ, θ) is a parametric model of the unknown function Nature(x) with parameters μ and θ, some of which are interesting (μ) and some not (θ). Likelihood L(μ, θ) = L(D | μ, θ) = P(D | μ, θ) D = observed data LPCC Workshop on Likelihoods CERN5

6. Glen: Basic Ideas Need a way to get rid of parameters not of current interest. There are two general ways, marginalization and profiling: Marginal Likelihood Profile Likelihood Profiling can be regarded as marginalization with the prior LPCC Workshop on Likelihoods CERN6

7. Kyle: Context & Scope LPCC Workshop on Likelihoods CERN7

8. Feedback

9. Marco: Is it the SM Higgs? LHC Higgs Cross Section Working Group Assumptions  SM tensor structure (CP-even scalar)  A single zero-width resonance  κ i = σ i / σ SMi and κ f = Γ f / Γ SMi are free parameters, where How do we best report experimental results (with the goal of allowing more detailed/accurate studies)? LPCC Workshop on Likelihoods CERN9

10. Maggie: Is it the SM Higgs? LPCC Workshop on Likelihoods CERN10 Can use an effective field theory (EFT) approach:

11. Maggie: Is it the SM Higgs? LPCC Workshop on Likelihoods CERN11

12. Béranger: Is it the SM Higgs? Effective Lagrangian Fitting procedure LPCC Workshop on Likelihoods CERN12

13. Béranger: Is it the SM Higgs? LPCC Workshop on Likelihoods CERN13

14. DAY 2 LPCC Workshop on Likelihoods CERN14

15. Kyle: HistFactory Equivalent to a multi-bin Poisson model with bins so small that the chance of > a single count per bin is negligible n is the number of events and {x e } are the measurements (e.g., the di-photon masses) In general, f is a mixture: LPCC Workshop on Likelihoods CERN15

16. Kyle: HistFactory which, in this case, represents a Gaussian G(x| μ, σ). f p (a p | α p ) are the likelihoods of the auxiliary measurements a p from either real, simulated, or hypothetical experiments. These functions provide constraints on the parameters α and hence on the parameters ν c (α). LPCC Workshop on Likelihoods CERN16

17. Kyle: HistFactory LPCC Workshop on Likelihoods CERN17 XML representation of model Kyle http://www.brianlemay.com/ HistFactory RooWorkspace

18. Sven: HZZ*(4l) in ATLAS LPCC Workshop on Likelihoods CERN18

19. Sven: HZZ*(4l) in ATLAS LPCC Workshop on Likelihoods CERN19 Cranmer, K, Kernel Estimation in High-Energy Physics Computer Physics Communications 136:198-207, 2001 hep ex/0011057 Kernel density estimation + density morphing + HistFactory

20. Sven: HZZ*(4l) in ATLAS LPCC Workshop on Likelihoods CERN20 Editorial comment: Jack’s intuition is spot on! For discrepant results, the combined result ought to be worse.

21. Sven: HZZ*(4l) in ATLAS Clarity Prize goes to Sven for explaining to me why a p-value computed from the background-only hypothesis depends on the alternative hypothesis! Harrison: “Please explain this plot” Sven: “The sampling distribution of t(x) = -2 ln L p /L max is independent of m H, as it should be, but the power of the test is maximized for each m H, so the observed value of t changes with m H ” LPCC Workshop on Likelihoods CERN21

22. Higgs Combination

23. Mingshui: Higgs Combination (CMS) Model: Marked Poisson Process (see Kyle’s HistFactory talk) LEP No constraints for parameters θ with systematic uncertainties Tevatron Use priors π(θ|θ 0 ) to constrain θ LHC Interpret π(θ|θ 0 ) as π(θ|θ 0 ) ~ f (θ 0 |θ) π(θ) Cowanscher Ur-prior! and interpret f (θ 0 |θ) as the likelihood for auxiliary measurements θ 0 LPCC Workshop on Likelihoods CERN23

24. Mingshui: Higgs Combination (CMS) Assumptions (current measurements)  Data are disjoint  Standard Model with m H and μ as free parameters  Same m H for all channels Detailed models can be provided in RooWorkspace form LPCC Workshop on Likelihoods CERN24

25. Haoshuang: Higgs Combination (ATLAS) Basic tool is HistFactory for all channels except for H to γγ A Single Channel LPCC Workshop on Likelihoods CERN25

26. Haoshuang: Higgs Combination (ATLAS) Important point In combining channels the Greek symbol fallacy is avoided. An explicit decision must be made about how parameters with the same name are related, if at all. Typically done by modifying the XML representation of the model. LPCC Workshop on Likelihoods CERN26

27. DAY 3 LPCC Workshop on Likelihoods CERN27

28. Wolfgang: BSM Searches Guided by a well-motivated theory, e.g., the pMSSM, and its simplified model decomposition pMSSM Results (non-CMS) …but CMS pMSSM / SMs analysis in progress… LPCC Workshop on Likelihoods CERN28

29. Wolfgang: BSM Searches LPCC Workshop on Likelihoods CERN29

30. Javier: BSM Searches LPCC Workshop on Likelihoods CERN30

31. Javier: BSM Searches LPCC Workshop on Likelihoods CERN31

32. Javier: BSM Searches LPCC Workshop on Likelihoods CERN32

33. Javier: BSM Searches LPCC Workshop on Likelihoods CERN33 Nuisance parameters marginalized through Monte Carlo integration

34. Wouter: RooFit RooFit is a probability modeling language: RooStats provides high level statistical tools that use RooFit models LPCC Workshop on Likelihoods CERN34

35. Wouter: RooFit A RooWorkspace is a mechanism to store a model + data LPCC Workshop on Likelihoods CERN35

36. Panel Discussion Sünje, Mike, Lorenzo HEPData on INSPIRE Make data sets searchable, findable, citable Assign Digital Object Identifier (DOI) to data  Should we track the re-use of data?  Should we have a single portal (e.g, Inspire)?  Will will have a single portal?  Will need non-web access also  RECAST requests that are honored could yield citation  Are there legal issues? LPCC Workshop on Likelihoods CERN36

37. CONCLUSIONS LPCC Workshop on Likelihoods CERN37

38. ICHEP 2040 LPCC Workshop on Likelihoods CERN38 Data pNMSSM OTTRTA SM m e, m μ, m τ m u, m d, m s, m c, m b, m t θ 12, θ 23, θ 13, δ g 1, g 2, g 3 θ QCD μ, λ The New Standard Model has been firmly established

39. Conclusions We could do a better job of understanding the LHC data if more information were made public in a systematic way A general way to do this is to publish the probability model + relevant data set The technology exists (RooWorkspace, Inspire, HepData) to publish arbitrarily complicated models, retrieve them and use them in analyses My sense is that our field is nearing a tipping point, for the better! LPCC Workshop on Likelihoods CERN39

40. Thanks!  We thank the LHC Physics Centre at CERN (LPCC) for hosting this workshop and its financial support of two RooStats developers. We thank the Theory Secretariat for organizing the coffee breaks!  We thank YOU for making this workshop both informative and enjoyable.  We thank the World’s funding agencies and the World’s taxpayers for their generous support: LHC cost: $1million / scientist LPCC Workshop on Likelihoods CERN40