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:
“Research shows clearly that parents who have modeled nurturant, reassuring responses to infants fears and distress by soothing words and stroking gentleness have toddlers who already can stroke a crying childs hair. Toddlers whose special adults model kindliness will even pick up a cookie dropped from a peers high chair and return it to the crying peer rather than eat it themselves!”
—Alice Sterling Honig (20th century)