Bayesian inference for PDFs
The determination of Parton Distribution Functions (PDFs) is an example of inverse problem: a model is sought knowing a finite set of experimental observations. Given the fact that the model is a continuous function, i.e. an element of an infinite dimensional space, its determination from a discrete set of data is notoriously a ill-posed problem. In the currently used methodologies for PDF determination, the model is parameterized in terms of a finite (albeit large) set of parameters, which are then fitted to the observed data. This procedure, known as parametric regression, reduces the problem to a finite dimensional and solvable one, but generally it has the drawback of introducing some bias. A Bayesian approach provides a suitable alternative to address inverse problems, avoiding the need to introduce a finite-dimensional parameterization and recasting the problem in a probabilistic language. I will discuss a Bayesian methodology for the determination of PDFs, providing examples for the determination of PDFs from Deep Inelastic Scattering data and from lattice matrix elements.
Wednesday, 6th December 2023, 14:30 — Sala Wataghin