Software for statistical data analysis used in Higgs searches

The analysis and interpretation of data collected by the Large Hadron Collider (LHC) requires advanced statistical tools in order to quantify the agreement between observation and theoretical models. RooStats is a project providing a statistical framework for data analysis with the focus on discoveries, confidence intervals and combination of different measurements in both Bayesian and frequentist approaches. It employs the RooFit data modelling language where mathematical concepts such as variables, (probability density) functions and integrals are represented as C++ objects. RooStats and RooFit rely on the persistency technology of the ROOT framework. The usage of a common data format enables the concept of digital publishing of complicated likelihood functions. The statistical tools have been developed in close collaboration with the LHC experiments to ensure their applicability to real-life use cases. Numerous physics results have been produced using the RooStats tools, with the discovery of the Higgs boson by the ATLAS and CMS experiments being certainly the most popular among them. We will discuss tools currently used by LHC experiments to set exclusion limits, to derive confidence intervals and to estimate discovery significances based on frequentist statistics and the asymptotic behaviour of likelihood functions. Furthermore, new developments in RooStats and performance optimisation necessary to cope with complex models depending on more than 1000 variables will be reviewed.