Parton distributions: determining probabilities in a space of functions

TL;DR

This paper analyzes the statistical properties of parton distribution functions using the NNPDF methodology, focusing on consistency, Bayesian behavior, and uncertainty estimation related to data and functional form inference.

Contribution

It introduces tests for statistical consistency, tools for data compatibility assessment, and quantifies uncertainties from data and functional form inference.

Findings

Results are independent of parametrization.

Results follow Bayes' theorem with new data.

Quantified uncertainties from data and functional form inference.

Abstract

We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the underlying parametrization and that it behaves according to Bayes' theorem upon the addition of new data. We then study the dependence of results on consistent or inconsistent datasets and present tools to assess the consistency of new data. Finally we estimate the relative size of the PDF uncertainty due to data uncertainties, and that due to the need to infer a functional form from a finite set of data.