  The Laser Interferometer Space Antenna will be the first Gravitational Wave
observatory in space. It is scheduled to fly in the early 2030's. LISA design
predicts sensitivity levels that enable the detection a Stochastic
Gravitational Wave Background signal. This stochastic type of signal is a
superposition of signatures from sources that cannot be resolved individually
and which are of various types, each one contributing with a different spectral
shape. In this work we present a fast methodology to assess the detectability
of a stationary, Gaussian, and isotropic stochastic signal in a set of
frequency bins, combining information from the available data channels. We
derive an analytic expression of the Bayes Factor between the instrumental
noise-only and the signal plus instrumental noise models, that allows us to
compute the detectability bounds of a given signal, as a function of frequency
and prior knowledge on the instrumental noise spectrum.
