# 10.5 Multidimensional analysis

Author(s): Jovan Veljanoski, Amina Helmi, Davide Massari, Maarten Breddels

We compare the statistical properties of four small regions on the sky by quantifying the degree of clustering and correlations between different observables, using the Kullback-Leibler divergence (KLD hereafter). This test allow us to establish whether any observables or a combination of thereof exhibit unexpected properties.

The selected regions on the sky are circular, have a radius of 5 ${}^{\circ}$, and for symmetry purposes are centred on ($l$,$b$) = (-90, -45), (-90, 45), (90, -45) and (90, 45). They are labelled ‘patch-a’, ‘patch-b’, ‘patch-c’, and ‘patch-d’, respectively. The regions contain $\sim$350 000 stars on average: ‘patch-a’ and ‘patch-d’ cover regions of high number of transits, while ‘patch-b’ and ‘patch-c’ have fewer transits. This choice reflects our expectation that different groups of observables will have differing distributions depending on the location on the sky, but also on the number of photometric or astrometric observations. For example Figure 10.32 shows how phot_g_n_obs varies across the field of each of the four patches.

We perform our tests also on a few subsets, as listed in Table 10.5. Furthermore, we have performed the KLD tests with and without the rescaling of the astrometric uncertainties by the factor $F$ used to reweight the uncertainties (Lindegren et al. 2018, Appendix A), but we found no differences.