Statistical Tools of Interstellar Turbulence: Bridging the Gap Between Numerics and Observations

MHD Turbulence is a critical component of the current paradigms of star formation, particle transport, magnetic reconnection and evolution of the ISM. Progress on this difficult subject is made via numerical simulations and observational studies. However, due to limitations of resolution, scale discrepancies, and complexity of the observations, the best approach for connecting numerics to observations is not always obvious. Here we advocate for a approach that invokes statistical techniques to understand the underlying physics of turbulent astrophysical systems. The wealth of numerical and observational data calls for new statistical tools to be developed in order to study turbulence in the interstellar medium. We briefly review some of the recently developed statistics that focus on characterizing gas compressibility and magnetization and their uses to interstellar studies.