INPP Seminar - Simonetta Liuti, University of Virgina

Beyond χ2: Likelihood, Correlations and Uncertainty in Hadron Physics Extracting the quark and gluon structure of hadrons from experiment involves successive inverse problems, in which the observables depend nonlinearly on multiple, strongly correlated, theoretical quantities. Conventional analyses based on (χ2) minimization and Hessian error estimates can provide an incomplete characterization of the solutions when the likelihood is non-Gaussian, exhibits degeneracies, or contains multiple modes. In this talk, I will discuss likelihood-based Bayesian inference and Markov Chain Monte Carlo (MCMC) methods for extracting Compton Form Factors from deeply virtual exclusive scattering measurements. Particular attention will be given to the role of parameter correlations, the structure of the likelihood, and the interpretation of uncertainties and credible intervals. By comparing conventional minimization techniques with posterior sampling, I will illustrate how different statistical approaches can lead to substantially different representations of the solutions allowed by the same experimental data, with implications for precision hadron imaging and future measurements at Jefferson Lab and the EIC.