Observations of exoplanetary transits and eclipses are a powerful tool to investigate the nature of planets around other stars. They are revealed through periodic drops in the apparent stellar brightness, due to the interposition of a planet between the star and the observer (transit) and occultation of the planet by the star (eclipse). The shape of an exoplanetary transit light-curve depends on the geometry of the star-planet-observer system and the spatial distribution of the stellar emission at the wavelength at which observations are taken (limb darkening profile).
Multi-wavelength observations are used to characterize the atmospheres of exoplanets through differences in the transit and eclipse depth at the level of one part in 10^4-5 in stellar flux. They have been successful in detecting the presence of atomic, ionic and molecular species over tens of transiting exoplanets. Current observatories, except Kepler, were not designed to achieve the required precision. Data reduction is necessary to minimize the effect of instrument systematics in order to achieve the target precision. Furthermore, stellar activity and other astrophysical signals may have similar amplitudes, hence need to be disentangled. In the past, parametric models have extensively been used by most teams to remove correlated noise with the aid of auxiliary information of the instrument, the so-called optical state vectors (OSVs). Such OSVs can include inter- and intra-pixel position of the star or its spectrum, instrument temperatures and inclinations, and/or other parameters. In some cases, different parametrizations led to discrepant results.

In the past four years the use of blind non-parametric data detrending techniques has proven successful to overcome those issues. During my PhD, I have pioneered the use of Independent Component Analysis (ICA)-based algorithms to extract the signal from photometric Spitzer/IRAC data (Morello et al. 2014, 2015, 2016; Morello 2015), and more recently from the Hubble/WFC3 spectroscopic observations (Damiano, Morello et al., in prep.). ICA is a blind source separation (BSS) technique which allows to disentangle the multiple instrument systematics and astrophysical signals in transit/eclipse light-curves. ICA does not require a model for the systematics, and for this reason, it can be applied to a variety of instruments with little changes, if any. E.g. ICA has been applied also to Kepler (Waldmann 2012), Hubble/NICMOS and Spitzer/IRS (Waldmann 2012, 2014, Waldmann et al. 2013) with excellent results.

In my talk, I will illustrate the ICA technique, the results of its application to exoplanetary transit and eclipse light-curves, and discuss the application of ICA and other non-parametric techniques developed by our team to stellar studies, e.g. asteroseismology and stellar activity. I will also discuss the importance of having accurate prior models and/or independent estimates of stellar and planetary parameters to break some degeneracies, and how they can be obtained with TESS and current observatories.