Parameter Identifiability
Overview
Parameter identifiability asks whether different parameter values or models can produce the same observations, and which aspects of a system can therefore be recovered. Researchers analyze symmetries and equivalence classes, use rank and Fisher-information conditions, and design informative experiments with sufficient excitation, diverse trajectories, or interventions. These ideas apply to dynamical systems, inverse problems, latent-variable models, and neural networks, where tools such as structural analysis, Bayesian inference, and constrained estimation help distinguish unique recovery from uncertainty or partial identification. A central tension is that accurate predictions do not guarantee uniquely or precisely identified parameters: structural ambiguities may persist regardless of data volume, while finite, noisy data can make even identifiable parameters difficult to estimate.
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