  Many exoplanets have orbital characteristics quite different from those seen
in our own solar system, including planets locked in orbital resonances and
planets on orbits that are elliptical or highly inclined from their host star's
spin axis. It is debated whether the wide variety in system architecture is
primarily due to differences in formation conditions (nature) or due to
evolution over time (nurture). Identifying trends between planetary and stellar
properties, including stellar age, can help distinguish between these competing
theories and offer insights as to how planets form and evolve. However, it can
be challenging to determine whether observed trends between planetary
properties and stellar age are driven by the age of the system -- pointing to
evolution over time being an important factor -- or other parameters to which
the age may be related, such as stellar mass or stellar temperature. The
situation is complicated further by the possibilities of selection biases,
small number statistics, uncertainties in stellar age, and orbital evolution
timescales that are typically much shorter than the range of observed ages.
Here we develop a Bayesian statistical framework to assess the robustness of
such observed correlations and to determine whether they are indeed due to
evolutionary processes, are more likely to reflect different formation
scenarios, or are merely coincidental. We apply this framework to reported
trends between stellar age and 2:1 orbital resonances, spin-orbit
misalignments, and hot Jupiters' orbital eccentricities. We find strong support
for the nurture hypothesis only in the final case.
