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Aims. Deriving accurate frequencies, amplitudes, and mode lifetimes fromstochastically driven pulsation is challenging, more so, if one demands thatrealistic error estimates be given for all model fitting parameters. As hasbeen shown by other authors, the traditional method of fitting Lorentzianprofiles to the power spectrum of time-resolved photometric or spectroscopicdata via the Maximum Likelihood Estimation (MLE) procedure delivers goodapproximations for these quantities. We, however, show that a conservativeBayesian approach allows one to treat the detection of modes with minimalassumptions (i.e., about the existence and identity of the modes).  Methods. We derive a conservative Bayesian treatment for the probability ofLorentzian profiles being present in a power spectrum and describe an efficientimplementation that evaluates the probability density distribution ofparameters by using a Markov-Chain Monte Carlo (MCMC) technique.  Results. Potentially superior to "best-fit" procedure like MLE, which onlyprovides formal uncertainties, our method samples and approximates the actualprobability distributions for all parameters involved. Moreover, it avoidsshortcomings that make the MLE treatment susceptible to the built-inassumptions of a model that is fitted to the data. This is especially relevantwhen analyzing solar-type pulsation in stars other than the Sun where theobservations are of lower quality and can be over-interpreted. As an example,we apply our technique to CoRoT observations of the solar-type pulsator HD49933.

On the detection of Lorentzian profiles in a power spectrum: A Bayesian approach using ignorance priors