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RooStats for Searches

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 Added by Gregory Schott
 Publication date 2012
  fields Physics
and research's language is English




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The RooStats toolkit, which is distributed with the ROOT software package, provides a large collection of software tools that implement statistical methods commonly used by the High Energy Physics community. The toolkit is based on RooFit, a high-level data analysis modeling package that implements various methods of statistical data analysis. RooStats enforces a clear mapping of statistical concepts to C++ classes and methods and emphasizes the ability to easily combine analyses within and across experiments. We present an overview of the RooStats toolkit, describe some of the methods used for hypothesis testing and estimation of confidence intervals and finally discuss some of the latest developments.



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RooStats is a project to create advanced statistical tools required for the analysis of LHC data, with emphasis on discoveries, confidence intervals, and combined measurements. The idea is to provide the major statistical techniques as a set of C++ classes with coherent interfaces, so that can be used on arbitrary model and datasets in a common way. The classes are built on top of the RooFit package, which provides functionality for easily creating probability models, for analysis combinations and for digital publications of the results. We will present in detail the design and the implementation of the different statistical methods of RooStats. We will describe the various classes for interval estimation and for hypothesis test depending on different statistical techniques such as those based on the likelihood function, or on frequentists or bayesian statistics. These methods can be applied in complex problems, including cases with multiple parameters of interest and various nuisance parameters.
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We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested fit to calculate the different probability distributions and other related quantities. Nested fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.
96 - N. J. Ayres , G. Ban , G. Bison 2019
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