https://doi.org/10.1140/epjc/s10052-024-13100-1
Regular Article - Theoretical Physics
Bayesian inference with Gaussian processes for the determination of parton distribution functions
1
Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
2
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, Peter Guthrie Tait Road, EH9 3 FD, Edinburgh, UK
3
Department of Physics and Astronomy, Vrije Universiteit, 1081 HV, Amsterdam, The Netherlands
4
Nikhef Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands
5
Dipartimento di Statistica, Informatica, Applicazioni “Giuseppe Parenti” (DISIA), Università di Firenze, Viale Morgagni 59, 50134, Firenze, Italy
Received:
7
May
2024
Accepted:
1
July
2024
Published online:
22
July
2024
We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian processes (GPs) are used to model the PDF prior, while Bayes’ theorem is used in order to determine the posterior distribution of the PDFs given a set of data. We discuss the general formalism, the Bayesian inference at the level of both parameters and hyperparameters, and the simplifications which occur when the observable entering the analysis is linear in the PDF. We benchmark the new methodology in two simple examples for the determination of a single PDF flavor from a set of deep inelastic scattering (DIS) data and from a set of equal-time correlators computed using lattice QCD. We discuss our results, showing how the proposed methodology allows for a well-defined statistical interpretation of the different sources of errors entering the PDF uncertainty, and how results can be validated a posteriori.
© The Author(s) 2024
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