Semi-supervised standardized detection of extrasolar planets

The detection of small exoplanets by the radial velocity (RV) technique is limited by various, not well-known, noise sources. As a consequence, current detection techniques often fail to provide reliable estimates of the "significance levels" of detection tests in terms of false alarm rates or of p-values. We aim at designing a RV detection procedure that provides reliable p-values estimates. The method incorporates ancillary information on the noise (e.g., stellar activity indicators), and specific data- or context-driven data (e.g., instrumental measurements, simulations of stellar variability) if available. The detection part of the procedure uses a detection test applied to a standardized periodogram. Standardization allows for an autocalibration of the noise sources with partially unknown statistics (Algorithm 1). The part regarding the estimation of the p-value of the test output is based on dedicated Monte Carlo simulations allowing to handle unknown parameters (Algorithm 2). The procedure is versatile in the sense that the specific couple (test, periodogram) is chosen by the user. We demonstrate by numerical experiments on synthetic and real RV data from the Sun and aCenB that the proposed methodology allows to robustly estimate the p-values. The method also provides a way to evaluate the dependence on modeling errors of the estimated p-values attributed to a reported detection, which is a critical point for RV planet detection at low signal-to-noise ratio. The python algorithms developed in this work are available on GitHub. Accurate estimation of p-values in the case where unknown parameters are involved in the detection process is an important yet newly addressed question in the field of RV detection. Although this work presents a method to this aim, the statistical literature discussed in this paper may trigger the development of other strategies.