# Identifiability

## (Statistical) Identifiability

The following definition is from (, , Section 2): Given a set of distributions \(\mathcal{ P }=\{p_\theta:\theta\in\Theta\}\) (\(\mathcal{ P }\) called a probabilistic model here) on some observational space \(\mathcal{ X }\), \(\mathcal{ P }\) is said to be identifiable if the mapping \(\theta\mapsto p_\theta(x)\) is injective, i.e. \(p_{\theta_1}(x)=p_{\theta_2}(x)\) for all \(x\in \mathcal{ X }\) implies \(\theta_1=\theta_2\).

Identifiability is a property of the probabilistic model, and not any estimation method.