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Group A: Limits and p-values with nuisance parameters Banff, July 2006

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1) Limits with nuisance parameters: Joel producing updated version of ‘challenge’ Different people to try different methods 1’) Kyle et al: Extended problem for LHC Higgs search 2) p-values: Long note by Luc

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Luc Demortier: 6 p-value questions for Statisticians Why 5 σ? Look-elsewhere and FDR? 8 methods for systematics and p-values. Optimal statistic? Non-standard L ratio: Importance sampling for 5 σ Fishing with Poisson: Use half data Alternatives to p-values? Posterior probabilities? Convenor for p-values

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Specific talks James Bueno: Calculator for Bayesian limits Tony Burnett: Looking for 5 σ sources in GLAST Lots of false sources. Tom Junk: Not necessarily disaster Eric Marchand: Lower limit on frequentist coverage for Bayes intervals for bounded continuous parameters Wants to extend to Poisson Example of HPD Bayes interval with 0% coverage for some θ Gunter Zech: Paradoxes about choosing between H1 and H2 via χ 2 or L -ratio

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Specific talks Giovanni Punzi: Fully frequentist method for Poisson + 1 nuisance param Little overcoverage Extendable to more parameters? Luc Demortier: Reference analysis Applied to Punzi problem of 1/p measurement

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Specific talks Kyle Cranmer: Marked Poisson for LHC Higgs Many channels Cranmer and Conrad: Profile L Full calculation with shapes slow, so use profile L to select candidates at ≥3 σ for full treatment Bodhi Sen: Conf intervals with nuisance parameters Also looks for signal (s > 0). But depends on prior for s=0, so better to look for N s ≠ 0. Working on coverage properties for Bayesian upper limits for Poisson with nuisance param Joel Heinrich: Turn Poisson with discrete n into continuous measurement of t

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Thank You! Weather forecasters BIRS and PIMS Participants for working at Workshop Statisticians for advice and patience Convenors: Joel, Luc, David, Byron, Nancy

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Thank You! Weather forecasters BIRS and PIMS Participants for working at Workshop Statisticians for advice and patience Convenors: Joel, Luc, David, Byron, Nancy Nancy

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