The issue of parameter identifiability is a pervasive one in determining model parameters from data, specifically in trying to answer whether unique parameter estimation is possible for a given problem. Many related definitions of identifiability with subtle distinctions can be found in existing literature, and in this talk, we highlight some of the most utilized versions of structural and practical identifiability in the context of dynamical systems. A differential algebra framework for structural identifiability is introduced for deriving input-output equations, and rank-revealing factorization algorithms for parameter subset selection are presented for practical identifiability purposes. These approaches together can more thoroughly characterize model parameters in dynamical systems and have important consequences for the parameter estimation problem.

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