  We use the most recent cosmic microwave background (CMB) data to perform a
Bayesian statistical analysis and discuss the observational viability of
inflationary models with a non-minimal coupling,~$\xi$, between the inflaton
field and the Ricci scalar. We particularize our analysis to two examples of
small and large field inflationary models, namely, the Coleman-Weinberg and the
chaotic quartic potentials. We find that (i) the $\xi$ parameter is closely
correlated with the primordial amplitude; (ii) although improving the agreement
with the CMB data in the $r - n_s$ plane, where $r$ is the tensor-to-scalar
ratio and $n_s$ the primordial spectral index, a non-null coupling is strongly
disfavoured with respect to the minimally coupled standard $\Lambda$CDM model,
since the upper bounds of the Bayes factor (odds) for $\xi$ parameter are
greater than $150:1$.
