Summary and Conclusions Kyle Cranmer (New York University)

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Summary and ConclusionsKyle Cranmer (New York University)

Harrison B. Prosper (Florida State University)Sezen Sekmen (CERN)

LPCC Workshop: Likelihoods for LHC Searches

LPCC Workshop on Likelihoods CERN

List of TalksDay 1

h Sezen Goalsh Glen Principlesh Kyle Context/Scope

Feedbackh Marcoh Maggieh Béranger

Day 2h Kyle HistFactoryh Sven ATLAS HZZ4lHiggs Combination h Minshui CMSh Haoshuang ATLAS

Day 3h Wolfgangh Javier (thanks Maurizio!)h WouterPanelists Sünje, Mike,

Lorenzo2LPCC Workshop on Likelihoods CERN

DAY 1

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Sezen: Workshop Goals

Goalsh Educate ourselves: why are likelihoods needed?h Move towards routine publication of likelihoods

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Glen: Basic Ideas

DistributionProbability density (or mass) function, Nature(x)x potential observations

ModelP(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).

LikelihoodL(μ, θ) = L(D | μ, θ) = P(D | μ, θ) D = observed data

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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

Lm (x | μ)= L(x |μ, θ)∫ π(θ)dθ

Lp (x | μ)=L(x |μ, ˆ̂θ(μ))

π (θ ) = δ (θ − ˆ̂θ )

Kyle: Context & Scope

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Feedback

Marco: Is it the SM Higgs?

LHC Higgs Cross Section Working GroupAssumptions

h SM tensor structure (CP-even scalar)h A single zero-width resonanceh 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)?

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€

σ ⋅BR(ii → H → ff ) = σ SM ⋅BRSM

κ i2 ⋅κ f

2

κ H2

Maggie: Is it the SM Higgs?

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Can use an effective field theory (EFT) approach:

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Maggie: Is it the SM Higgs?

Béranger: Is it the SM Higgs?

Effective Lagrangian

Fitting procedure

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Béranger: Is it the SM Higgs?

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DAY 2

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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:

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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).

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Kyle: HistFactory

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XML representation of model

Kyle

http://www.brianlemay.com/

HistFactory

RooWorkspace

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Sven: HZZ*(4l) in ATLAS

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Sven: HZZ*(4l) in ATLAS

Cranmer, K, Kernel Estimation in High-Energy Physics Computer Physics Communications 136:198-207, 2001hep ex/0011057

Kernel density estimation+ density morphing+ HistFactory

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Sven: HZZ*(4l) in ATLAS

Editorial comment: Jack’s intuition is spot on! For discrepantresults, the combined result ought to be worse.

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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 distributionof t(x) = -2 ln Lp/Lmax is independentof mH, as it should be, but the powerof the test is maximized for each mH,so the observed value of t changes with mH”

Higgs Combination

Mingshui: Higgs Combination (CMS)

Model: Marked Poisson Process (see Kyle’s HistFactory talk)LEP

No constraints for parameters θ with systematic uncertainties

TevatronUse priors π(θ|θ0) to constrain θ

LHCInterpret 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

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Mingshui: Higgs Combination (CMS)

Assumptions (current measurements)h Data are disjointh Standard Model with mH and μ as free parametersh Same mH for all channels

Detailed models can be provided in RooWorkspace formLPCC Workshop on Likelihoods CERN 24

Haoshuang: Higgs Combination (ATLAS)

Basic tool is HistFactory for all channels except for H to γγA Single Channel

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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.

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DAY 3

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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…

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Wolfgang: BSM Searches

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Javier: BSM Searches

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Javier: BSM Searches

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Javier: BSM Searches

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Javier: BSM Searches

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Nuisance parametersmarginalized throughMonte Carlo integration

Wouter: RooFit

RooFit is a probability modeling language:

RooStats provides high level statistical tools that use RooFit models

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Wouter: RooFit

A RooWorkspace is a mechanism to store a model + data

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Panel Discussion

Sünje, Mike, Lorenzo

HEPData on INSPIRE Make data sets searchable, findable, citableAssign Digital Object Identifier (DOI) to datah Should we track the re-use of data?h Should we have a single portal (e.g, Inspire)?h Will will have a single portal?h Will need non-web access alsoh RECAST requests that are honored could yield citationh Are there legal issues?

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CONCLUSIONS

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ICHEP 2040

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Data

pNMSSM

OTTRTA

p(Data | Theory)

SMme, mμ, mτ

mu, md, ms, mc, mb, mt

θ12, θ23, θ13, δg1, g2, g3

θQCD

μ, λ

The New Standard Model has been firmly established

p(Theory | Data)

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!

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Thanks!

h 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!

h We thank YOU for making this workshop both informative and enjoyable.

h We thank the World’s funding agencies and the World’s taxpayers for their generous support:

LHC cost: $1million / scientist

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