Identifying unidentifiability
Leutenant Cauchy: Sir, we have an unidentified parameter entering regression airspace.
Admiral Gauss: Can we reparameterize and obtain their identity?
Leutenant Cauchy: Trying now, Sir. No success.
Admiral Gauss: Do we have any prior information?
Leutenant Cauchy: No, Sir.
Admiral Gauss: Shoot it down…
What is identifiability?
Formal definition
A statistical model \(\mathcal{P} = \{P_\theta: \theta \in \Theta\}\) is identifiable if the mapping of \(\theta \to P_\theta\) is one-to-one and invertible.