Sparsely Sampling the Sky: Regular vs Random Sampling

Abstract: 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.