Kriging Interpolating Cosmic Velocity Field
  [abridged] Volume-weighted statistics of large scale peculiar velocity is
preferred by peculiar velocity cosmology, since it is free of uncertainties of
galaxy density bias entangled in mass-weighted statistics. However, measuring
the volume-weighted velocity statistics from galaxy (halo/simulation particle)
velocity data is challenging. For the first time, we apply the Kriging
interpolation to obtain the volume-weighted velocity field. Kriging is a
minimum variance estimator. It predicts the most likely velocity for each place
based on the velocity at other places. We test the performance of Kriging
quantified by the E-mode velocity power spectrum from simulations. Dependences
on the variogram prior used in Kriging, the number $n_k$ of the nearby
particles to interpolate and the density $n_P$ of the observed sample are
investigated. First, we find that Kriging induces $1\%$ and $3\%$ systematics
at $k\sim 0.1h{\rm Mpc}^{-1}$ when $n_P\sim 6\times 10^{-2} ({\rm Mpc}/h)^{-3}$
and $n_P\sim 6\times 10^{-3} ({\rm Mpc}/h)^{-3}$, respectively. The deviation
increases for decreasing $n_P$ and increasing $k$. When $n_P\lesssim 6\times
10^{-4} ({\rm Mpc}/h)^{-3}$, a smoothing effect dominates small scales, causing
significant underestimation of the velocity power spectrum. Second, increasing
$n_k$ helps to recover small scale power. However, for $n_P\lesssim 6\times
10^{-4} ({\rm Mpc}/h)^{-3}$ cases, the recovery is limited. Finally, Kriging is
more sensitive to the variogram prior for lower sample density. The most
straightforward application of Kriging on the cosmic velocity field does not
show obvious advantages over the nearest-particle method (Zheng et al. 2013)
and could not be directly applied to cosmology so far. However, whether
potential improvements may be achieved by more delicate versions of Kriging is
worth further investigation.
