Bayesian parameter estimation in chiral effective field theory using the Hamiltonian Monte Carlo method

The number of low-energy constants (LECs) in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) grows rapidly with increasing order, necessitating the use Markov chain Monte Carlo techniques for sampling their posterior probability density function. For this we introduce a Hamiltonian (HMC) algorithm and sample LEC up to next-to-next-to-leading order (NNLO) two-nucleon sector $\ensuremath{\chi}\mathrm{EFT}$. We find that efficiency HMC is three six times higher compared an affine-invariant algorithm. analyze empirical coverage validate NNLO model yields predictions scattering data largely reliable credible intervals, provided one ignores leading-order EFT expansion parameter when inferring variance truncation error. also error dominates budget.