Space science from a directional statistical point of view

It should be no surprise that already back in the 17th and 18th centuries important foundations of modern statistical theory were formulated to address astronomical problems, the astronomers were the statisticians. This has given rise to the research flow called astrostatistics, which has been particularly
active over the past decades. However, with the increasing amount of astronomical data nowadays, the need for more innovative modern statistical theories and models is required. Directional statistics, a branch of statistics involving observations such as directions, axes, rotations, etc. with values on (compact) Riemannian manifolds -- not, as in classical multivariate statistical analysis, unrestricted $\mathbb{R}^d$-valued vectors ($d \geq 1$) -- like our celestial sphere, has shown a promising involvement to deal and address with important space science issues such as space weather, cosmology, or even space surveillance. Thus providing interesting insights to protect our Earth but also furthering our understanding of the Universe we inhabit.

In this paper, we will instigate directional statistics by providing a review of their old and recent developments simulated by interesting applications in space science.