NumberCountingUtils Namespace Reference

RooStats standalone utilities. More...

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

Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void value

Double_t Exp(Double_t x)

Returns the base-e exponential function of x, which is e raised to the power x.