Parametric Model

A parametric model is a collection of probability distributions such that each member of this collection, Pθ, is described by a finite-dimensional parameter θ. The set of all allowable values for the parameter is denoted Θ ⊆ Rk, and the model itself is written as

\mathcal{P} = \big\{ P_\theta\ \big|\ \theta\in\Theta \big\}.

When the model consists of absolutely continuous distributions, it is often specified in terms of corresponding probability density functions:

\mathcal{P} = \big\{ f_\theta\ \big|\ \theta\in\Theta \big\}.

The parametric model is called identifiable if the mapping θ ↦ Pθ is invertible, that is there are no two different parameter values θ1 and θ2 such that Pθ1 = Pθ2.

Read more about Parametric Model:  Regular Parametric Model, See Also

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