A continuous multiple hypothesis testing framework for optimal exoplanet detection

Abstract: The detection of exoplanets is hindered by the presence of complex astrophysical and instrumental noises. Given the difficulty of the task, it is important to ensure that the data are exploited to their fullest potential. In the present work, we search for an optimal exoplanet detection criterion. We adopt a general Bayesian multiple hypothesis testing framework, where the hypotheses are indexed by continuous variables. This framework is adaptable to the different observational methods used to detect exoplanets as well as other data analysis problems. We describe the data as a combination of several parametrized patterns and nuisance signals. We wish to determine which patterns are present, and for a detection to be valid, the parameters of the claimed pattern have to correspond to a true one with a certain accuracy. We search for a detection criterion 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, the two approaches lead to the same optimal procedure. We apply it 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.