We use two different methods, Monte Carlo sampling and variational inference (VI), to perform a Bayesian calibration of the effective-range parameters in ${ }^3$He-${ }^4$He elastic scattering. The parameters are calibrated to data from a recent set of $^{ 3}$He-${ }^4$He elastic scattering differential cross section measurements. Analysis of these data for $E_{ \rm lab} \leq 4.3$ MeV yields a unimodal posterior for which both methods obtain the same structure. However, the effective-range expansion amplitude does not account for the $7/2^-$ state of ${ }^7$Be so, even after calibration, the description of data at the upper end of this energy range is poor. The data up to $E_{ \rm lab}=2.6$ MeV can be well described, but calibration to this lower-energy subset of the data yields a bimodal posterior. After adapting VI to treat such a multi-modal posterior we find good agreement between the VI results and those obtained with parallel-tempered Monte Carlo sampling.
Categories: nucl-th stat.AP