# P-values and Bayesian limits and CLs limits and fits for new physics searches using ROOT -- mclimit_csm.C

C++

Major Toolset

Hypothesis Tester

This package is designed to compute p-values and also Bayesian and CLs limits, combining one or more search results in the form of histograms if data, and signal and background predictions. The signal and background may be sums of several componenents, each with its own set of systematic uncertainties. Categories of uncertainties considered are: rate uncertainties, shape uncertainties, and MC(or data) statistics in each bin. In order to optimize the sensitivity of the likelihood ratio test statistic, MINUIT fits are performed, both on the data and on pseudoexperiments. A null hypothesis and a test hypothesis are fit separately to the (pseudo)data, and the ratio of the resulting likelihood fits is used as a test statistic for computing p-values and CLs. Different model predictions may be used to generate pseudoexperiments and to fit. Systematic errors are categorized by name, with errors with the same name considered to be correlated, errors with different names considered to be uncorrelated. A set of histogram interpolation tools is provided inside for 1D and 2D histograms. Limits to compute Bayesian limits are provided using the same model inputs. Updates include cross section fitters, expected cross section uncertainty calculators, and a 2D cross section fitter.

Thomas R. Junk Joel Heinrich with contributions from Alex Read Tom Wright Kevin Lannon

trj@fnal.gov

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