Reliable inference of exoplanet light-curve parameters using deterministic and stochastic systematics models

Time series photometry and spectroscopy of transiting exoplanets allow us to study their atmospheres. Unfortunately, the required precision to extract atmospheric information surpasses the design specifications of most general purpose instrumentation, resulting in instrumental systematics in the light curves that are typically larger than the target precision. Systematics must therefore be modelled, leaving the inference of light-curve parameters conditioned on the subjective choice of systematics models and model selection criteria. This paper aims to test the reliability of the most commonly used deterministic systematics models and model selection criteria. As we are primarily interested in recovering light-curve parameters rather than the favoured systematics model, marginalization over systematics models is introduced as a more robust alternative than simple model selection. This can incorporate uncertainties in the choice of systematics model into the error budget as well as the model parameters. Its use is demonstrated using a series of simulated transit light curves. Stochastic models, specifically Gaussian processes, are also discussed in the context of marginalization over systematics models, and are found to reliably recover the transit parameters for a wide range of systematics functions. None of the tested model selection criteria - including the Bayesian information criterion - routinely recovered the correct model. This means that commonly used methods that are based on simple model selection may underestimate the uncertainties when extracting transmission and eclipse spectra from real data, and low significance claims using such techniques should be treated with caution. In general, no systematics modelling techniques are perfect; however, marginalization over many systematics models helps to mitigate poor model selection, and stochastic processes provide an even more flexible approach to modelling instrumental systematics.