  We use the most recent type Ia supernovae (SNe Ia) observations to perform a
statistical comparison between the standard $\Lambda$CDM model and its
extensions [$w$CDM and $w(z)$CDM] and some alternative cosmologies: namely, the
Dvali--Gabadadze--Porrati (DGP) model, a power-law $f(R)$ scenario in the
metric formalism and an example of vacuum decay [$\Lambda(t)$CDM] cosmology in
which the dilution of pressureless matter is attenuated with respect to the
usual $a^{-3}$ scaling due to the interaction of the dark matter and dark
energy fields. We perform a Bayesian model selection analysis using the
\textsc{MultiNest} algorithm. To obtain the posterior distribution for the
parameters of each model, we use the joint light-curve analysis (JLA) SNe Ia
compilation containing 740 events in the interval $0.01 < z < 1.3$ along with
current measurements of baryon acoustic oscillations (BAO). The JLA data are
analyzed with the SALT2 light-curve fitter and the model selection is then
performed by computing the Bayesian evidence of each model and the Bayes factor
of the $\Lambda$CDM cosmology related to the other models. The results indicate
that the JLA data alone are unable to distinguish the standard $\Lambda$CDM
model from some of its alternatives but its combination with current
measurements of baryon acoustic oscillations shows up an ability to distinguish
them. In particular, the DGP model is practically not supported by both the BAO
and the joint JLA + BAO data sets compared to the standard scenario. Finally,
we provide a rank order for the models considered.
