Bayesian Approach to Inverse Problems: an Application to NNPDF Closure Testing

Understand

We discuss the Bayesian approach to the solution of inverse problems and apply the formalism to analyse the closure tests performed by the NNPDF collaboration.

• Starting from a comparison with the approach that is currently used for the determination of parton distributions (PDFs) by the NNPDF collaboration, we discuss some analytical results that can be obtained for linear problems and use these results as a guidance for the more complicated non-linear problems.
• We show that, in the case of Gaussian distributions, the posterior probability density of the parametrized PDFs is fully determined by the results of the NNPDF fitting procedure.
• In the particular case that we consider, the fitting procedure and the Bayesian analysis yield exactly the same result.