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When searching for exoplanets, one wants to count how many planets orbit agiven star, and to determine what their orbital parameters are. If theestimated orbital elements are too far from those of a planet truly present,this should be considered as a false detection. This setting is a particularinstance of a general one: aiming to retrieve which parametric components arein a dataset corrupted by nuisance signals, with a certain accuracy on theirparameters. We exhibit a detection criterion minimizing false and misseddetections, either as a function of their relative cost, or when the expectednumber of false detections is bounded. If the components can be separated in atechnical sense discussed in detail, the optimal detection criterion is aposterior probability obtained as a by-product of Bayesian evidencecalculations, and we discuss how it can be calibrated. We show on twosimulations emulating exoplanet searches that it can significantly outperformother criteria. Finally, we show that our framework offers solutions for theidentification of components of mixture models, and Bayesian false discoveryrate control when hypotheses are not discrete.

A continuous multiple hypothesis testing framework for optimal exoplanet detection