Kernel estimation in high-energy physics

By Kyle S. Cranmer. 2000

488 citations recorded by the source corpus.

Kernel estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of kernel estimation is developed for univariate and multivariate settings. The second section discusses some of the applications of kernel estimation to high-energy physics. The third section provides an overview of the available univariate and multivariate packages. This paper concludes with a discussion of the inherent advantages of kernel estimation techniques and systematic errors associated with the estimation of parent distributions.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4d240e57f7ab8381e212187c04d0ba94561d2968

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Citations in the corpus

First combination of Tevatron and LHC measurements of the top-quark mass (2014, background): “Further details are provided in the following sections.”
Measurement of angular parameters from the decay B0 → K⁎0μ+μ− in proton–proton collisions at s=8TeV (2017, methodology): “The numerator and denominator of the efficiency are separately described with a nonparametric technique, which is implemented with a kernel density estimator [48,49].”
Measurements of the properties of the Higgs-like boson in the four lepton decay channel with the ATLAS detector using 25 fb$^{-1}$ of proton-proton collision data (2013, methodology): “The mass distributions are described using smooth, non-parametric, unbinned estimates [85] of the relevant probability density functions obtained from simulation.”
Search for the Standard Model Higgs Boson at LEP (2001, methodology): “In order to avoid problems which might arise in some bins due to low Monte Carlo statistics, smoothing procedures such as [22] are applied which use the corresponding information in the neighbouring bins.”
Measurement of the $J/\psi$ pair production cross-section in $pp$ collisions at $\sqrt{s} = 13 \,{\mathrm{TeV}}$ (2016, methodology): “The uncertainty due to the signal shape description is estimated by replacing the nominal model with two alternative models, the Hypatia function [86] and a kernel estimate for the underlying probability distribution function of the simulated sample convolved with a Gaussian function [87].”
Study of the spin and parity of the Higgs boson in diboson decays with the ATLAS detector (2015, unknown): “To obtain a reliable description for bins with an insufficient number of Monte Carlo events, the Kernel Density Estimation [43] smoothing procedure is applied to signal and background multi-dimensional histograms.”
Test of lepton universality with B0 → K*0ℓ+ℓ− decays (2017, methodology): “The former are described using a kernel estimation technique [54] applied to simulated events for which the K+π− invariant mass distribution has been matched to data from ref.”
Search for exclusive Higgs and Z boson decays to ϕγ and ργ with the ATLAS detector (2017, methodology): “The nominal selection requirements are imposed on the ensemble and the surviving pseudocandidates are used to construct templates for the mMγ distribution, which are then smoothed using Gaussian kernel density estimation [62].”
Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of nu(e) interactions at the far detector (2017, unknown): “A kernel density estimator (KDE) [82, 83], is used to extract the most probable values of the oscillation parameters of interest, A KDE PDF is built by smearing the step points with a Gaussian function which has a width inversely proportional to the number of points.”
The RooFit Toolkit for Data Modeling (2003, background): “There is no limit to the number of observables in the event generator, but the presence of groups of two, three or more of observables that do not factorize will impact the performance of the accept/reject technique due to phase-space considerations.”
Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with 6.6E20 protons on target (2015, methodology): “SKDETSIM incorporates the propagation of 072010-25 photons in water, subject to absorption, Rayleigh scattering, and Mie scattering.”
Test of lepton flavor universality by the measurement of the branching fraction using three-prong decays (2017, methodology): “To study this effect, a method based on the use of kernel density estimators (KDE) [48] is used.”