Efficient sampling of Bayesian posteriors and predictive distributions in χEFT

Sammanfattning: In this thesis I employ Bayesian statistics to quantify parametric and epistemic uncertainties in chiral effective field theories (χEFT) and propagate these forward to predictions of observables in low-energy nuclear physics. Two primary sources of uncertainty---experimental errors and the theoretical error induced by the truncation of the EFT at up to next-to-next-to-leading-order---are modelled and accounted for in the posterior distributions of the unknown low-energy constants (LECs) that govern interaction strengths in χEFT. These posteriors are computationally challenging to extract and I therefore introduce an advanced Markov chain Monte Carlo (MCMC) algorithm, known as Hamiltonian Monte Carlo, and investigate its performance. I compare its sampling efficiency to standard MCMC algorithms and find reductions in computation time by factors around 3-6 in the present work. I exploit the extracted posteriors to produce predictive distributions for neutron-proton and proton-proton scattering cross sections below and above the pion production threshold and check the consistency of the model predictions against empirical data and higher-order point estimates. I find that the predictive distributions provide reliable credibility intervals as long as the size of the truncation error is estimated from expansion coefficients at next-to-leading-order and above. The LEC posteriors are also central to uncertainty quantification in few- and manybody systems, and as part of a larger collaboration I explore constraints on three-nucleon forces imposed by light-nuclei observables.