the true probability distribution P0 in the model, and since the identifiability condition above requires that the map be invertible, we will also be able to find the true value of the parameter which generated given distribution P0. Examples Example 1 Let be the normal location-scale family: Then This expression is equal to zero for almost all x only when all its coefficients are equal to zero, which is only possible when |σ1| = |σ2| and μ1 = μ2. Since in the scale parameter σ is restricted to be greater than zero, we conclude that the model is identifiable: ƒθ1 = ƒθ2 ⇔ θ1 = θ2. Example 2 Let be the standard linear regression model: (where ′ denotes matrix transpose). Then the parameter β is identifiable if and only if the matrix is invertible. Thus, this is the identification condition in the model. Example 3 Suppose is the classical errors-in-variables linear model: where (ε,η,x*) are jointly normal independent random variables with zero expected value and unknown variances, and only the variables (x,y) are observed. Then this model is not identifiable, only the product βσ²∗ is (where σ²∗ is the variance of the latent regressor x*). This is also an example of a set identifiable model: although the exact value of β cannot be learned, we can guarantee that it must lie somewhere in the interval (βyx, 1÷βxy), where βyx is the coefficient in OLS regression of y on x, and βxy is the coefficient in OLS regression of x on y. If we abandon the normality assumption and require that x* were not normally distributed, retaining only the independence condition ε ⊥ η ⊥ x*, then the model becomes identifiable. See also Observability System identification Simultaneous equations model References Citations Sources Further reading Econometrics Estimation theory