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Information geometric complexity of entropic motion on curved statistical manifolds

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.