Bayesian Inference with Gaussian Processes for the Determination of Parton Distribution Functions

TL;DR

This paper introduces a Bayesian approach using Gaussian Processes to determine parton distribution functions, providing a statistically rigorous framework for uncertainty quantification and validation in high-energy physics data analysis.

Contribution

The paper presents a novel Bayesian methodology employing Gaussian Processes for PDF determination, including hyperparameter inference and validation techniques, applicable to DIS and lattice QCD data.

Findings

Effective uncertainty quantification for PDFs

Validation of the methodology with DIS and lattice QCD data

Enhanced statistical interpretation of PDF errors

Abstract

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.