On posterior probability and significance level: application to the power spectrum of HD 49 933 observed by CoRoT

Context. The CoRoT mission provides asteroseismic data of very high quality allowing one to adopt new statistical approaches for mode detection in power spectra, especially with respect to testing the null hypothesis ((0), which assumes that what is observed is pure noise). Aims. We emphasize that the significance level when rejecting the null hypothesis can lead to the incorrect conclusion that the H(0) hypothesis is unlikely to occur at that significance level. We demonstrate that the significance level is unrelated to the posterior probability of H(0), given the observed data set, and that this posterior probability is very much higher than implied by the significance level. Methods. We use Bayes theorem to derive the posterior probability of that H(0) is true assuming an alternative hypothesis H(1) that a mode is present, taking some prior for the mode height, mode amplitude and linewidth. Results. We compute the posterior probability of H(0) for the p modes detected on HD 49 933 by CoRoT. Conclusions. We conclude that the posterior probability of H(0) provide a much more conservative quantification of the mode detection than the significance level. This framework can be applied to any similar stellar power spectra obtained to complete asteroseismology.