  We quantify the posterior predictive distributions (PPDs) of elastic
neutron-deuteron ($nd$) scattering cross sections using nucleon-nucleon ($NN$)
interactions from chiral effective field theory ($\chi$EFT) up to and including
next-to-next-to-next-to-leading order (N$^3$LO). These PPDs quantify the spread
in $nd$ predictions due to the variability of the low-energy constants (LECs)
inferred from $NN$ scattering data. We use the wave-packet continuum
discretization method to solve the Alt-Grassberger-Sandhas form of the Faddeev
equations for elastic scattering. We draw 100 samples from the PPDs of $nd$
cross sections up to 67 MeV in scattering energy, i.e., in the energy region
where the effects of three-nucleon forces are expected to be small. We find
that the uncertainty about $NN$ LECs inferred from $NN$ scattering data, when
assuming uncorrelated errors, does not translate to significant uncertainty in
the low-energy $nd$ continuum. Based on our estimates, the uncertainty of $nd$
predictions are dominated by the $\chi$EFT truncation error, at least below
N$^3$LO. At this order, the 90% credible interval of the PPD and the truncation
error are comparable, although both are very small on an absolute scale.
