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
When the model consists of absolutely continuous distributions, it is often specified in terms of corresponding probability density functions:
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
Famous quotes containing the word model:
“She represents the unavowed aspiration of the male human being, his potential infidelity—and infidelity of a very special kind, which would lead him to the opposite of his wife, to the “woman of wax” whom he could model at will, make and unmake in any way he wished, even unto death.”
—Marguerite Duras (b. 1914)