NumberCountingUtils Namespace Reference

RooStats standalone utilities. More...

Detailed Description

RooStats standalone utilities.

These are RooStats standalone utilities that calculate the p-value or Z value (eg. significance in 1-sided Gaussian standard deviations) for a number counting experiment. This is a hypothesis test between background only and signal-plus-background. The background estimate has uncertainty derived from an auxiliary or sideband measurement.

This is based on code and comments from Bob Cousins and on the following papers:

• Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process
  Authors: Robert D. Cousins, James T. Linnemann, Jordan Tucker
  http://arxiv.org/abs/physics/0702156
  NIM A 595 (2008) 480–501
  
• Statistical Challenges for Searches for New Physics at the LHC
  Authors: Kyle Cranmer
  http://arxiv.org/abs/physics/0511028
• Measures of Significance in HEP and Astrophysics
  Authors: J. T. Linnemann
  http://arxiv.org/abs/physics/0312059

The problem is treated in a fully frequentist fashion by interpreting the relative background uncertainty as being due to an auxiliary or sideband observation that is also Poisson distributed with only background. Finally, one considers the test as a ratio of Poisson means where an interval is well known based on the conditioning on the total number of events and the binomial distribution.

In short, this is an exact frequentist solution to the problem of a main measurement x distributed as a Poisson around s+b and a sideband or auxiliary measurement y distributed as a Poisson around tau*b. Eg.

\[ L(x,y|s,b,\tau) = Pois(x|s+b) Pois(y|\tau b) \]

Naming conventions:
Exp = Expected
Obs = Observed
P   = p-value
Z   = Z-value or significance in sigma (one-sided convention)