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Advanced Statistical Methods with Nuisance Parameters: Insights from Banff 2006 Workshop

This document presents a summary of the Banff workshop held in July 2006, focusing on statistical methodologies involving nuisance parameters. It features discussions on limits, p-values, and various statistical techniques such as Bayesian intervals, Poisson models, and frequentist approaches. Key topics include exploring the implications of nuisance parameters in LHC Higgs searches, optimal statistical methods, and alternative approaches to p-values. The contributions from notable statisticians such as Joel, Luc, and Tony provide valuable perspectives on the ongoing challenges in this field.

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Advanced Statistical Methods with Nuisance Parameters: Insights from Banff 2006 Workshop

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  1. Group A: Limits and p-valueswith nuisance parameters Banff, July 2006

  2. 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

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

  4. Specific talks James Bueno: Calculator for Bayesian limits Tony Burnett: Looking for 5σ 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 χ2 or L-ratio

  5. 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

  6. 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 ≥3σfor 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 Ns ≠ 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

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

  8. 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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