  Physical systems behave according to their underlying dynamical equations
which, in turn, can be identified from experimental data. Explaining data
requires selecting mathematical models that best capture the data regularities.
Identifying dynamical equations from the available data and statistical model
selection are both very difficult tasks. Motivated by these fundamental links
among physical systems, dynamical equations, experimental data and statistical
modeling, we discuss in this invited Contribution our information geometric
measure of complexity of geodesic paths on curved statistical manifolds
underlying the entropic dynamics of classical physical systems described by
probability distributions. We also provide several illustrative examples of
entropic dynamical models used to infer macroscopic predictions when only
partial knowledge of the microscopic nature of the system is available.
Finally, we present entropic arguments to briefly address complexity softening
effects due to statistical embedding procedures.
