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

Abstract

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