  Barium (Ba) stars help to verify asymptotic giant branch (AGB) star
nucleosynthesis models since they experienced pollution from an AGB binary
companion and thus their spectra carry the signatures of the slow neutron
capture process (s process). For 180 Ba stars, we searched for AGB stellar
models that match the observed abundance patterns. We employed three machine
learning algorithms as classifiers: a Random Forest method, developed for this
work, and the two classifiers used in our previous study. We studied the
statistical behaviour of the s-process elements in the observational sample to
investigate if the AGB models systematically under- or overpredict the
abundances observed in the Ba stars and show the results in the form of violin
plots of the residuals between spectroscopic abundances and model predictions.
We find a significant trend in the residuals that implies an underproduction of
the elements Nb, Mo, and Ru in the models relative to the observations. This
may originate from a process (e.g. the intermediate neutron-capture process, i
process) at the metallicity of the Ba stars not yet included in the AGB models.
Correlations are found between the residuals of these elements, suggesting a
common origin for the deviations. In addition, there is a weak metallicity
dependence of their residuals. The s-process temperatures derived with the
[Zr/Fe] - [Nb/Fe] thermometer have an unrealistic value for the majority of our
stars. The most likely explanation is that at least a fraction of these
elements are not produced in a steady-state s process, and instead may be due
to processes not included in the AGB models. The mass distribution of the
identified models confirms that our sample of Ba stars was polluted by low-mass
AGB stars. Most of the matching AGB models require low accreted mass, but a few
systems with high accreted mass are needed to explain the observations.
(abridged)
