Identifiability
Property of a model indicating whether its parameters can be uniquely determined from available experimental data.
Identifiability is the mathematical property that determines whether the parameters of a model can be uniquely inferred from a given set of observations 1.
How It Works
A model is structurally identifiable if, given perfect noise-free data from all observable outputs, each parameter has a unique value. Structural identifiability is assessed through analytical methods — differential algebra, Taylor series approaches, or generating series — applied to the model equations before any data is collected 2.
Practical identifiability goes further by asking whether parameters can be reliably estimated given realistic, noisy, finite data. Profile likelihood analysis is a standard approach: each parameter is fixed at different values while the remaining parameters are re-optimized, revealing whether the likelihood surface has a well-defined minimum or flat ridges indicating non-identifiability 1.
Non-identifiable parameters signal that the model is overparameterized for the available data. Remedies include simplifying the model, reparameterizing with identifiable combinations, or designing new experiments that constrain the ambiguous parameters.
Computational Considerations
Symbolic computation packages such as DAISY and STRIKE-GOLDD automate structural identifiability tests for ODE models. For practical identifiability, profile likelihood computations scale with the number of parameters and may require parallel optimization. Active learning and reinforcement learning approaches can suggest optimal experiments that maximally resolve non-identifiable parameters 2.
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Structural identifiability analysis uses symbolic computation, while practical identifiability leverages profile likelihoods and Fisher information; ML aids optimal experiment design.