Unfolding with Gaussian Processes. / Bozson, Adam; Cowan, Glen; Spanò, Francesco.

In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 03.11.2018.

Research output: Contribution to journalArticle

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Unfolding with Gaussian Processes. / Bozson, Adam; Cowan, Glen; Spanò, Francesco.

In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 03.11.2018.

Research output: Contribution to journalArticle

Harvard

Bozson, A, Cowan, G & Spanò, F 2018, 'Unfolding with Gaussian Processes', Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment.

APA

Bozson, A., Cowan, G., & Spanò, F. (2018). Unfolding with Gaussian Processes. Manuscript submitted for publication.

Vancouver

Bozson A, Cowan G, Spanò F. Unfolding with Gaussian Processes. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 2018 Nov 3.

Author

Bozson, Adam ; Cowan, Glen ; Spanò, Francesco. / Unfolding with Gaussian Processes. In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 2018.

BibTeX

@article{182b050a0dd440e087ac7788e74e6a97,
title = "Unfolding with Gaussian Processes",
abstract = "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. ",
keywords = "physics.data-an, Unfolding, Gaussian Processes",
author = "Adam Bozson and Glen Cowan and Francesco Span{\`o}",
note = "7 pages, 6 figures. Submitted to NIM A",
year = "2018",
month = nov,
day = "3",
language = "English",
journal = "Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment",
issn = "0168-9002",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Unfolding with Gaussian Processes

AU - Bozson, Adam

AU - Cowan, Glen

AU - Spanò, Francesco

N1 - 7 pages, 6 figures. Submitted to NIM A

PY - 2018/11/3

Y1 - 2018/11/3

N2 - 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.

AB - 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.

KW - physics.data-an

KW - Unfolding

KW - Gaussian Processes

M3 - Article

JO - Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment

JF - Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment

SN - 0168-9002

ER -