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Glen Cowan

Publications and source records attributed to Glen Cowan.

14 recordsLinked to original sources
arXiv2026

Discovery Sensitivity for a Counting Experiment with Background Uncertainty

In Particle Physics, a search for a new signal process is often based on observing a Poisson-distributed number of events, whose mean contains contributions from background and, if it exists, the hypothesised signal. The discovery significance can be expressed as an equivalent number of standard deviations derived from the $p$-value of the background-only hypothesis. To characterise the experimental sensitivity, one may report the median, assuming a nominal signal strength, of the discovery significance. In this paper, approximate expressions for the median significance are derived both when the expected number of background events is known and when the background rate is uncertain but constrained by a Poisson control measurement. The formulae are based on a test statistic using the profile likelihood ratio, and the median significance is approximated using the Asimov data set. Higher-order asymptotic corrections, based on the Barndorff-Nielsen $r^\ast$ statistic, are incorporated for both the observed and expected discovery significance. The validity of the resulting expressions is compared with Monte Carlo results and with other formulae for expected significance often used in particle physics. The higher-order corrections are found to provide meaningful improvements at small event yields. The results are important for obtaining an accurate assessment of the sensitivity of a planned experiment and for the optimal choice of cuts that determine the expected numbers of signal and background events.

physics.data-an↗
arXiv2025

Correlated Systematic Uncertainties and Errors-on-Errors in Measurement Combinations: Methodology and Application to the 7-8 TeV ATLAS-CMS Top Quark Mass Combination

The Gamma Variance Model (GVM) is a statistical model that incorporates uncertainties in the assignment of systematic errors (informally called errors-on-errors). The model is of particular use in analyses that combine the results of several measurements. In the past, combinations have been carried out using two alternative approaches: the Best Linear Unbiased Estimator (BLUE) method or what we will call the nuisance-parameter method. In this paper we derive useful relations that allow one to connect the BLUE and nuisance-parameter methods when the correlations induced by systematic uncertainties are non-trivial (1, -1 or 0), and we generalise the nuisance-parameter approach to include errors-on-errors. We then illustrate some of the properties of the GVM by applying it to the 7-8 TeV ATLAS-CMS top quark mass combination. We present results by considering the largest systematic uncertainties as uncertain, one at a time, and we vary their associated error-on-error parameters. This procedure is useful for identifying the systematic uncertainties to which a combination is sensitive when they are themselves uncertain. We also explore the hypothetical scenario of including an outlier in the combination, which could become relevant for future combinations, by artificially adding a fictitious measurement to it. This example highlights a key feature of the GVM: its sensitivity to the internal consistency of the input data.

hep-ex↗
arXiv2024

Higher-order asymptotic corrections and their application to the Gamma Variance Model

We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can incorporate uncertainties in parameters that themselves represent uncertainties (informally, "errors on errors") called the Gamma Variance Model. This model contains fixed parameters, generically called $\varepsilon$, that represent the relative uncertainties in estimates of standard deviations of Gaussian distributed measurements. If the $\varepsilon$ parameters are small, one can construct confidence intervals and $p$-values using standard asymptotic methods. This is formally similar to the familiar situation of a large data sample, in which estimators for all adjustable parameters have Gaussian distributions. Here we address the important case where the $\varepsilon$ parameters are not small and as a consequence the asymptotic distributions do not represent a good approximation. We investigate improved test statistics based on the technology of higher-order asymptotics ($p^*$ approximation and Bartlett correction).

physics.data-an↗
arXiv2021

Publishing statistical models: Getting the most out of particle physics experiments

The statistical models used to derive the results of experimental analyses are of incredible scientific value and are essential information for analysis preservation and reuse. In this paper, we make the scientific case for systematically publishing the full statistical models and discuss the technical developments that make this practical. By means of a variety of physics cases -- including parton distribution functions, Higgs boson measurements, effective field theory interpretations, direct searches for new physics, heavy flavor physics, direct dark matter detection, world averages, and beyond the Standard Model global fits -- we illustrate how detailed information on the statistical modelling can enhance the short- and long-term impact of experimental results.

hep-ph↗
arXiv2021

Effect of Systematic Uncertainty Estimation on the Muon $g-2$ Anomaly

The statistical significance that characterizes a discrepancy between a measurement and theoretical prediction is usually calculated assuming that the statistical and systematic uncertainties are known. Many types of systematic uncertainties are, however, estimated on the basis of approximate procedures and thus the values of the assigned errors are themselves uncertain. Here the impact of the uncertainty {\it on the assigned uncertainty} is investigated in the context of the muon $g-2$ anomaly. The significance of the observed discrepancy between the Standard Model prediction of the muon's anomalous magnetic moment and measured values are shown to decrease substantially if the relative uncertainty in the uncertainty assigned to the Standard Model prediction exceeds around 30\%. The reduction in sensitivity increases for higher significance, so that establishing a $5σ$ effect will require not only small uncertainties but the uncertainties themselves must be estimated accurately to correspond to one standard deviation.

hep-ph↗
arXiv2020

Comparison of unfolding methods using RooFitUnfold

In this paper we describe RooFitUnfold, an extension of the RooFit statistical software package to treat unfolding problems, and which includes most of the unfolding methods that commonly used in particle physics. The package provides a common interface to these algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. In this paper we exploit this common interface of RooFitUnfold to compare the performance of unfolding with the Richardson-Lucy, Iterative Dynamically Stabilized, Tikhonov, Gaussian Process, Bin-by-bin and inversion methods on several example problems.

physics.data-an↗
arXiv2019

Statistical Models with Uncertain Error Parameters

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable with a given standard deviation (the corresponding "systematic error"). Although the assigned systematic errors are usually treated as constants, in general they are themselves uncertain. A type of model is presented where the uncertainty in the assigned systematic errors is taken into account. Estimates of the systematic variances are modeled as gamma distributed random variables. The resulting confidence intervals show interesting and useful properties. For example, when averaging measurements to estimate their mean, the size of the confidence interval increases for decreasing goodness-of-fit, and averages have reduced sensitivity to outliers. The basic properties of the model are presented and several examples relevant for Particle Physics are explored.

physics.data-an↗
arXiv2018

Unfolding with Gaussian Processes

A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents are distributed approximately according to a Gaussian, this estimator is equivalent to the mean function of a GP conditioned on the maximum likelihood estimator. Regularisation is introduced via the kernel function of the GP, which has a natural interpretation as the covariance of the underlying distribution. This novel approach allows for the regularisation to be informed by prior knowledge of the underlying distribution, and for it to be varied along the spectrum. In addition, the full statistical covariance matrix for the estimator is obtained as part of the result. The method is applied to two examples: a double-peaked bimodal distribution and a falling spectrum.

physics.data-an↗
arXiv2013

Statistics for Searches at the LHC

These lectures describe several topics in statistical data analysis as used in High Energy Physics. They focus on areas most relevant to analyses at the LHC that search for new physical phenomena, including statistical tests for discovery and exclusion limits. Particular attention is payed to the treatment of systematic uncertainties through nuisance parameters.

hep-ex↗
arXiv2013

Asymptotic formulae for likelihood-based tests of new physics

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 account 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.

physics.data-an↗
arXiv2011

Power-Constrained Limits

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.

physics.data-an↗
arXiv2001

Present and Future CP Measurements

We review theoretical and experimental results on CP violation summarizing the discussions in the working group on CP violation at the UK phenomenology workshop 2000 in Durham.

hep-ph↗
arXiv1997

Two Photon Physics at LEP2

The working group on two photon physics concentrated on three main subtopics: modelling the hadronic final state of deep inelastic scattering on a photon; unfolding the deep inelastic scattering data to obtain the photon structure function; and resonant production of exclusive final states, particularly of glueball candidates. In all three areas, new results were presented.

hep-ph↗