A continuous multiple hypothesis testing framework for optimal exoplanet detection

When searching for exoplanets, one wants to count how many planets orbit a given star, and to determine what their orbital parameters are. If the estimated orbital elements are too far from those of a planet truly present, this should be considered as a false detection. This setting is a particular instance of a general one: aiming to retrieve which parametric patterns are in a dataset corrupted by nuisance signals, with a certain accuracy on their parameters. We search for a decision rule minimizing false and missed detections, either as a function of their relative cost, or when the expected number of false detections is bounded. We find that if the patterns can be separated in a technical sense, it is sufficient to select the parameter regions with highest posterior probability. We then discuss how the obtained posterior probabilities can be calibrated. We apply our procedure to the retrieval of periodic signals in unevenly sampled time series, emulating the search for exoplanets in radial velocity data. We show on a simulation that, for a given tolerance to false detections, the new criterion leads to 15 to 30\% more true detections than other criteria, including the Bayes factor.