Summary and Conclusions Kyle Cranmer (New York University)

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

2. List of Talks Day 1 • Sezen Goals • Glen Principles • Kyle Context/ScopeFeedback • Marco • Maggie • Béranger Day 2 • Kyle HistFactory • Sven ATLAS HZZ4l Higgs Combination • Minshui CMS • Haoshuang ATLAS Day 3 • Wolfgang • Javier (thanks Maurizio!) • Wouter PanelistsSünje, Mike, Lorenzo LPCC Workshop on Likelihoods CERN

3. Day 1 LPCC Workshop on Likelihoods CERN

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

5. Glen: Basic Ideas Distribution Probability density (or mass) function, Nature(x) x potential 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 CERN

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 CERN

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

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 • κi = σi / σSMi and κf = Γf / ΓSMi are free parameters, where How do we best report experimental results (with the goal of allowing more detailed/accurate studies)? LPCC Workshop on Likelihoods CERN

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

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

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

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

14. Day 2 LPCC Workshop on Likelihoods CERN

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 {xe} are the measurements (e.g., the di-photon masses) In general, f is a mixture: LPCC Workshop on Likelihoods CERN

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

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

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

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

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

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 lnLp/Lmax is independent of mH, as it should be, but the power of the test is maximized for eachmH, so the observed value of t changes with mH” LPCC Workshop on Likelihoods CERN

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|θ0) to constrain θ LHC Interpret π(θ|θ0) as π(θ|θ0) ~ f(θ0|θ) π(θ) Cowanscher Ur-prior! and interpret f(θ0|θ) as the likelihood for auxiliary measurements θ0 LPCC Workshop on Likelihoods CERN

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

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

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 CERN

27. Day 3 LPCC Workshop on Likelihoods CERN

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 CERN

29. Wolfgang: BSM Searches LPCC Workshop on Likelihoods CERN

30. Javier: BSM Searches LPCC Workshop on Likelihoods CERN

31. Javier: BSM Searches LPCC Workshop on Likelihoods CERN

32. Javier: BSM Searches LPCC Workshop on Likelihoods CERN

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

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

35. Wouter: RooFit ARooWorkspace is a mechanism to store a model + data LPCC Workshop on Likelihoods CERN

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 CERN

37. Conclusions LPCC Workshop on Likelihoods CERN

38. ICHEP 2040 The New Standard Model has been firmly established pNMSSM me, mμ, mτ mu, md, ms, mc, mb, mt θ12, θ23, θ13, δ g1, g2, g3 θQCD μ, λ SM OTTRTA Data LPCC Workshop on Likelihoods CERN

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 CERN

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 CERN