In the effort to characterize the masses, radii, and atmospheres of potentially habitable exoplanets, there is an urgent need to find examples of such planets transiting nearby M dwarfs. The MEarth Project is an ongoing effort to do so, as a ground-based photometric survey designed to detect exoplanets as small as 2 R ⊕ transiting mid-to-late M dwarfs within 33?pc of the Sun. Unfortunately, identifying transits of such planets in photometric monitoring is complicated both by the intrinsic stellar variability that is common among these stars and by the nocturnal cadence, atmospheric variations, and instrumental systematics that often plague Earth-bound observatories. Here, we summarize the properties of MEarth data gathered so far, emphasizing the challenges they present for transit detection. We address these challenges with a new framework to detect shallow exoplanet transits in wiggly and irregularly spaced light curves. In contrast to previous methods that clean trends from light curves before searching for transits, this framework assesses the significance of individual transits simultaneously while modeling variability, systematics, and the photometric quality of individual nights. Our Method for Including Starspots and Systematics in the Marginalized Probability of a Lone Eclipse (MISS MarPLE) uses a computationally efficient semi-Bayesian approach to explore the vast probability space spanned by the many parameters of this model, naturally incorporating the uncertainties in these parameters into its evaluation of candidate events. We show how to combine individual transits processed by MISS MarPLE into periodic transiting planet candidates and compare our results to the popular box-fitting least-squares method with simulations. By applying MISS MarPLE to observations from the MEarth Project, we demonstrate the utility of this framework for robustly assessing the false alarm probability of transit signals in real data.
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