Nonidentifiability

Nonidentifiability occurs when observed data do not uniquely determine a model’s parameters. A model is identifiable if different parameter values produce distinct data distributions; otherwise, multiple parameter vectors are consistent with the data. Nonidentifiability can be global, meaning no parameter values yield distinct distributions, or local, where only nearby values are indistinguishable. It also distinguishes structural identifiability (theoretical) from practical identifiability (given finite, noisy data).

Causes include symmetries and redundancies in the model, overparameterization, missing measurements, and inadequate experimental design. In dynamic models, different parameter sets can generate the same output trajectory; in mixture models, permuting component labels leaves the likelihood unchanged, causing label switching and nonidentifiability of component parameters.

Consequences can include unstable parameter estimates and difficulties in interpreting parameters, though some predictions or identifiable parameter combinations may remain reliable. Approaches to address nonidentifiability include reparameterization, fixing or constraining parameters, or using informative priors in Bayesian analysis. Structural identifiability assessment (via methods such as DAISY or GenSSI) complements practical identifiability studies that rely on data quality and quantity.

Examples include mixture models with label switching and certain pharmacokinetic or epidemiological models with limited data. Recognizing and mitigating nonidentifiability is important for model selection, experimental design, and drawing credible conclusions from quantitative analyses.