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Identifiability refers to the property of a statistical model or system whereby its underlying parameters can be uniquely determined from observed data. In essence, if a model is identifiable, then the data generated by that model can only have arisen from a single set of parameter values. If multiple sets of parameters can produce the same observed data, then the model is not identifiable.

This concept is crucial in fields like econometrics, systems biology, and machine learning. When a model is not identifiable, it becomes impossible to reliably estimate the true values of its parameters, even with an infinite amount of data. This can lead to ambiguous conclusions and hinder scientific progress.

There are two main types of identifiability: structural identifiability and practical identifiability. Structural identifiability is a theoretical property that holds true regardless of the amount of data available. It depends solely on the structure of the model and the relationships between its parameters and the observed outputs. Practical identifiability, on the other hand, concerns whether the parameters can be estimated with sufficient precision given a finite and potentially noisy dataset. A model might be structurally identifiable but not practically identifiable if the data provides very little information about certain parameters.

Diagnosing and addressing identifiability issues is a key step in model building and analysis. Techniques such as sensitivity analysis and analyzing the Fisher information matrix can help determine if a model is identifiable. If a model is found to be unidentifiable, modifications to the model structure, the inclusion of more informative data, or imposing prior knowledge might be necessary.