The issue of detecting abnormal vibrations is addressed in this article, when little is known both on the mechanical behavior of the system, and on the characteristic patterns of potential faults. With data from a bearing test rig and from an aircraft engine, we show that when only a small learning set is available, Bayesian inference has several advantages in order to compute a model of healthy vibrations, and thus ensure fault detection. To do so, we compute the wavelet transform of many log-periodograms, and show that their probability density can be easily modelled. This allows us to compute a likelihood index when a new log-periodogram is presented, thanks to marginal likelihood approximation. A by-product of this computation is the ability to generate random log-periodograms according to the learning dataset probability density. Finally, we first detect the degradation of a bearing on a test rig; then we generate random samples of aircraft engine log-periodograms.