**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Shape-Constrained Uncertainty Quantification In Unfolding Steeply Falling Elementary Particle Spectra

Abstract

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from measurements smeared by the finite resolution of the particle detectors. Previous unfolding methods use ad hoc discretization and regularization, resulting in confidence intervals that can have significantly lower coverage than their nominal level. Instead of regularizing using a roughness penalty or stopping iterative methods early, we impose physically motivated shape constraints: positivity, monotonicity, and convexity. We quantify the uncertainty by constructing a nonparametric confidence set for the true spectrum, consisting of all those spectra that satisfy the shape constraints and that predict the observations within an appropriately calibrated level of fit. Projecting that set produces simultaneous confidence intervals for all functionals of the spectrum, including averages within bins. The confidence intervals have guaranteed conservative frequentist finite-sample coverage in the important and challenging class of unfolding problems for steeply falling particle spectra. We demonstrate the method using simulations that mimic unfolding the inclusive jet transverse momentum spectrum at the LHC. The shape-constrained intervals provide usefully tight conservative inferences, while the conventional methods suffer from severe undercoverage.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts

Loading

Related publications

Loading

Related publications (5)

Loading

Loading

Loading

This thesis studies statistical inference in the high energy physics unfolding problem, which is an ill-posed inverse problem arising in data analysis at the Large Hadron Collider (LHC) at CERN. Any measurement made at the LHC is smeared by the finite resolution of the particle detectors and the goal in unfolding is to use these smeared measurements to make nonparametric inferences about the underlying particle spectrum. Mathematically the problem consists in inferring the intensity function of an indirectly observed Poisson point process. Rigorous uncertainty quantification of the unfolded spectrum is of central importance to particle physicists. The problem is typically solved by first forming a regularized point estimator in the unfolded space and then using the variability of this estimator to form frequentist confidence intervals. Such confidence intervals, however, underestimate the uncertainty, since they neglect the bias that is used to regularize the problem. We demonstrate that, as a result, conventional statistical techniques as well as the methods that are presently used at the LHC yield confidence intervals which may suffer from severe undercoverage in realistic unfolding scenarios. We propose two complementary ways of addressing this issue. The first approach applies to situations where the unfolded spectrum is expected to be a smooth function and consists in using an iterative bias-correction technique for debiasing the unfolded point estimator obtained using a roughness penalty. We demonstrate that basing the uncertainties on the variability of the bias-corrected point estimator provides significantly improved coverage with only a modest increase in the length of the confidence intervals, even when the amount of bias-correction is chosen in a data-driven way. We compare the iterative bias-correction to an alternative debiasing technique based on undersmoothing and find that, in several situations, bias-correction provides shorter confidence intervals than undersmoothing. The new methodology is applied to unfolding the Z boson invariant mass spectrum measured in the CMS experiment at the LHC. The second approach exploits the fact that a significant portion of LHC particle spectra are known to have a steeply falling shape. A physically justified way of regularizing such spectra is to impose shape constraints in the form of positivity, monotonicity and convexity. Moreover, when the shape constraints are applied to an unfolded confidence set, one can regularize the length of the confidence intervals without sacrificing coverage. More specifically, we form shape-constrained confidence intervals by considering all those spectra that satisfy the shape constraints and fit the smeared data within a given confidence level. This enables us to derive regularized unfolded uncertainties which have by construction guaranteed simultaneous finite-sample coverage, provided that the true spectrum satisfies the shape constraints. The uncertainties are conservative, but still usefully tight. The method is demonstrated using simulations designed to mimic unfolding the inclusive jet transverse momentum spectrum at the LHC.

Related concepts (13)

In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level i

Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. U

Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or

Mikael Johan Kuusela, Victor Panaretos

We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising in data analysis at the Large Hadron Collider at CERN consists in estimating the intensity function of an indirectly observed Poisson point process. Unfolding typically proceeds in two steps: one first produces a regularized point estimate of the unknown intensity and then uses the variability of this estimator to form frequentist confidence intervals that quantify the uncertainty of the solution. In this paper, we propose forming the point estimate using empirical Bayes estimation which enables a data-driven choice of the regularization strength through marginal maximum likelihood estimation. Observing that neither Bayesian credible intervals nor standard bootstrap confidence intervals succeed in achieving good frequentist coverage in this problem due to the inherent bias of the regularized point estimate, we introduce an iteratively bias-corrected bootstrap technique for constructing improved confidence intervals. We show using simulations that this enables us to achieve nearly nominal frequentist coverage with only a modest increase in interval length. The proposed methodology is applied to unfolding the Z boson invariant mass spectrum as measured in the CMS experiment at the Large Hadron Collider.

Vladislav Balagura, Aurelio Bay, Marc-Olivier Bettler, Frédéric Blanc, Joël Bressieux, Peter Clarke, Victor Coco, Greig Alan Cowan, Michel De Cian, Hans Dijkstra, Frédéric Guillaume Dupertuis, Christoph Frei, Guido Haefeli, Plamen Hristov Hopchev, Pierre Jaton, Anne Keune, Ilya Komarov, Yiming Li, Johan Luisier, Maurizio Martinelli, Raluca Anca Muresan, Bastien Luca Muster, Tatsuya Nakada, Matthew Needham, Niko Neufeld, Cédric Potterat, Jessica Prisciandaro, Barinjaka Rakotomiaramanana, Gerhard Raven, Julien Rouvinet, Christophe Salzmann, Olivier Schneider, Liang Sun, Frédéric Teubert, Mark Tobin, Minh Tâm Tran, Jian Wang, Jean Wicht, Songmei Wu, Yi Zhang, Lei Zhang

This paper reports the first measurement of the effective B-S(0) -> J/psi K-S(0) lifetime and an updated measurement of its time-integrated branching fraction. Both measurements are performed with a data sample, corresponding to an integrated luminosity of 1.0 fb(-1) of pp collisions, recorded by the LHCb experiment in 2011 at a centre-of-mass energy of 7 TeV. The results are: tau(eff)(J/psi KS0) = 1.75 +/- 0.12 (stat) +/- 0.07 (syst) ps and B(B-S(0) -> J/psi K-S(0)) = (1.97 +/- 0.23) x 10(-5). For the latter measurement, the uncertainty includes both statistical and systematic sources. (C) 2013 CERN. Published by Elsevier B.V. All rights reserved.