  We perform a Bayesian model selection analysis for different classes of
phenomenological coupled scenarios of dark matter and dark energy with linear
and non-linear interacting terms. We use a combination of some of the latest
cosmological data such as type Ia supernovae (SNe Ia), cosmic chronometers
(CC), cosmic microwave background (CMB) and two sets of baryon acoustic
oscillations measurements, namely, 2-dimensional angular measurements (BAO2)
and 3-dimensional angle-averaged measurements (BAO3). We find weak and moderate
evidence against two-thirds of the interacting scenarios considered with
respect to $\Lambda$CDM when the full joint analysis is considered. About
one-third of the models provide a description to the data as good as the one
provided by the standard model. Our results also indicate that either SNe Ia,
CC or BAO2 data by themselves are not able to distinguish among interacting
models or $\Lambda$CDM but the standard BAO3 measurements and the combination
with the CMB data are indeed able to discriminate among them. We find that
evidence disfavoring interacting models is weaker when we use BAO2 (data
claimed to be almost model-independent) instead of the standard BAO3
measurements. These results help select classes of viable and non-viable
interacting models in light of current data.
