We develop a technique to present Higgs coupling measurements, which decouple the poorly defined theoretical uncertainties associated to inclusive and exclusive cross section predictions. The technique simplifies the combination of multiple measureme
nts and can be used in a more general setting. We illustrate the approach with toy LHC Higgs coupling measurements and a collection of new physics models.
We present the asymptotic distribution for two-sided tests based on the profile likelihood ratio with lower and upper boundaries on the parameter of interest. This situation is relevant for branching ratios and the elements of unitary matrices such as the CKM matrix.
We propose a method for setting limits that avoids excluding parameter values for which the sensitivity falls below a specified threshold. These power-constrained limits (PCL) address the issue that motivated the widely used CLs procedure, but do so
in a way that makes more transparent the properties of the statistical test to which each value of the parameter is subjected. A case of particular interest is for upper limits on parameters that are proportional to the cross section of a process whose existence is not yet established. The basic idea of the power constraint can easily be applied, however, to other types of limits.
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++ c
lasses 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.
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to acc
ount for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the Asimov data set, which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.
