Sparsely Sampling the Sky: Regular vs Random Sampling
  The next generation of galaxy surveys, aiming to observe millions of
galaxies, are expensive both in time and cost. This raises questions regarding
the optimal investment of this time and money for future surveys. In a previous
work, it was shown that a sparse sampling strategy could be a powerful
substitute for the contiguous observations. However, in this previous paper a
regular sparse sampling was investigated, where the sparse observed patches
were regularly distributed on the sky. The regularity of the mask introduces a
periodic pattern in the window function, which induces periodic correlations at
specific scales. In this paper, we use the Bayesian experimental design to
investigate a random sparse sampling, where the observed patches are randomly
distributed over the total sparsely sampled area. We find that, as there is no
preferred scale in the window function, the induced correlation is evenly
distributed amongst all scales. This could be desirable if we are interested in
specific scales in the galaxy power spectrum, such as the Baryonic Acoustic
Oscillation (BAO) scales. However, for constraining the overall galaxy power
spectrum and the cosmological parameters, there is no preference over regular
or random sampling. Hence any approach that is practically more suitable can be
chosen and we can relax the regular-grid condition for the distribution of the
observed patches.
