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Time-series photometry and spectroscopy of transiting exoplanets allow us tostudy their atmospheres. Unfortunately, the required precision to extractatmospheric information surpasses the design specifications of most generalpurpose instrumentation, resulting in instrumental systematics in the lightcurves that are typically larger than the target precision. Systematics musttherefore be modelled, leaving the inference of light curve parametersconditioned on the subjective choice of models and model selection criteria.This paper aims to test the reliability of the most commonly used systematicsmodels and model selection criteria. As we are primarily interested inrecovering light curve parameters rather than the favoured systematics model,marginalisation over systematics models is introduced as a more robustalternative than simple model selection. This can incorporate uncertainties inthe choice of systematics model into the error budget as well as the modelparameters. Its use is demonstrated using a series of simulated transit lightcurves. Stochastic models, specifically Gaussian processes, are also discussedin the context of marginalisation over systematics models, and are found toreliably recover the transit parameters for a wide range of systematicsfunctions. None of the tested model selection criteria - including the BIC -routinely recovered the correct model. This means that commonly used methodsthat are based on simple model selection may underestimate the uncertaintieswhen extracting transmission and eclipse spectra from real data, andlow-significance claims using such techniques should be treated with caution.In general, no systematics modelling techniques are perfect; however,marginalisation over many systematics models helps to mitigate poor modelselection, and stochastic processes provide an even more flexible approach tomodelling instrumental systematics.

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