Spectroscopic and spectropolarimetric observations with high spectral resolution provide extremely rich information on the physical conditions of distant celestial objects; sometimes, even the mere presence of a spectroscopic or polarimetric pattern may offer fundamental insights. But these are photon-starving techniques. Signals are often at the noise level or buried in it and, many times, just detection proves difficult. Here we present a Bayesian technique for the detection of spectropolarimetric signals based on the application of the non-parametric relevance vector machine to the observations, which allows computing the evidence for the presence of a signal and its most probable value.