In this work, we present a geometric approach, approximating the original log-likelihood by geodesic coordinates of the model manifold. In contrast, any method based on a Taylor expansion of the log-likelihood around the optimum, e.g., parameter uncertainty estimation by the Fisher Information Matrix, reveals no information about the boundedness at all. This situation, denoted as practical non-identifiability, can be detected by Monte Carlo sampling or by systematic scanning using the profile likelihood method. This means that along certain paths in parameter space, the log-likelihood does not exceed a given statistical threshold but remains bounded. When non-linear models are fitted to experimental data, parameter estimates can be poorly constrained albeit being identifiable in principle.
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