The Epoch of Reionisation (EoR), when the first light sources in the Universe ionise the atoms of the surrounding IGM, is a very active field of research in Cosmology and Astrophysics. The timeline and morphology of the EoR are precious sources of information about the young Universe and its first bright objects. Many ambitious observational projects are ongoing to target this information, from next-generation ground-based CMB observatories to ever bigger radio telescopes, such as the SKA. In order to use this future data optimally, a better knowledge of observational limitations and a better modelling of the reionisation process in itself are required.
In this talk, I will present statistical tools which aim at improving the analysis and interpretation of this data, namely by including more precise models of reionisation physics, and to construct a coherent analysis framework for EoR observables. First, I will introduce a novel model to derive analytically the kSZ angular power spectrum, shedding light on the impact of EoR on the small-scale CMB temperature power spectrum. Using SPT measurements (Reichardt+2021), we are able to extract cosmological information from previously disregarded CMB foregrounds and help constrain the timeline of cosmic reionisation. But one cannot speak of observing the EoR without considering the 21cm signal. Targeting the astrophysical information encompassed in the shape of ionisation bubbles throughout the EoR, and focusing on the spatial fluctuations of the 21cm signal, I will present novel statistical tools, designed to be robust to observational effects, and which can be a useful addition to the traditional power spectrum, especially within large MCMC analyses.