Bayesian Methods for Global PDF and EFT Analyses

In this talk I will discuss recent progress in Bayesian methods for global determinations of Parton Distribution Functions (PDFs) and their extension to joint analyses of PDFs and Standard Model  (SM) and beyond-the-Standard-Model (BSM) parameters.

In particular, I will present Colibri, an open-source Python framework for flexible and modular PDF fitting, allowing custom parametrizations and efficient computation of collider observables. Colibri provides unified access to experimental data and supports Hessian, Monte Carlo replica, and numerical Bayesian sampling methods. I will illustrate its potential for a systematic model selection and model averaging for benchmarking and combining different PDF parametrizations.

I will then address the interplay between proton structure and new physics searches, focusing on the possibility that standard PDF fits may partially absorb signals in high-energy observables. I will present a framework for the simultaneous determination of PDFs and Effective Field Theory (EFT) Wilson coefficients and outline a program towards fully Bayesian global analyses with controlled priors and consistent treatment of correlations, relevant for precision phenomenology at the LHC, HL-LHC, and future colliders.