  We examine the (3+1)-class of 4-neutrino mass spectra within a rigorous
statistical analysis based on the Bayesian approach to probability. The data of
the Bugey, CDHS and KARMEN experiments are combined by using a likelihood
function. Our statistical approach allows us to incorporate solar and
atmospheric neutrino data and also the result of the CHOOZ experiment via
inequalities which involve elements of the neutrino mixing matrix and are
derived from these data. For any short-baseline $\Delta m^2$ we calculate a
bound on the LSND transition amplitude $A_{\mu;e}$ and find that, in the
$\Delta m^2$--$A_{\mu;e}$ plane, there is no overlap between the 99% CL region
allowed by the latest LSND analysis and the region allowed by our bound on
$A_{\mu;e}$ at 95% CL; there are some small overlap regions if we take the
bound at 99% CL. Therefore, we conclude that, with the existing data, the
(3+1)-neutrino mass spectra are not very likely. However, treating the
(2+2)-spectra with our method, we find that they are well compatible with all
data.
