Kriging interpolating cosmic velocity field. II. Taking anistropies and
  multistreaming into account
  Measuring the volume-weighted peculiar velocity statistics from
inhomogeneously and sparsely distributed galaxies/halos, by existing velocity
assignment methods, suffers from a significant sampling artifact. As an
alternative, the Kriging interpolation based on Gaussian processes was
introduced and evaluated [Y. Yu, J. Zhang, Y. Jing, and P. Zhang, Phys. Rev. D
92, 083527 (2015)]. Unfortunately, the most straightforward application of
Kriging does not perform better than the existing methods in the literature. In
this work, we investigate two physically motivated extensions. The first takes
into account of the anisotropic velocity correlations. The second introduces
the nugget effect, on account of multi-streaming of the velocity field. We find
that the performance is indeed improved. For sparsely sampled data
[$n_P\lesssim 6\times 10^{-3}(h^{-1} {\rm Mpc})^{-3}$] where the sampling
artifact is the most severe, the improvement is significant and is two-fold: 1)
The scale of reliable measurement of the velocity power spectrum is extended by
a factor $\sim 1.6$, and 2) the dependence on the velocity correlation prior is
weakened by a factor of $\sim 2$. We conclude that such extensions are
desirable for accurate velocity assignment by Kriging.
