Estimators Based on a Probability Distribution for the Parameters

Abstract

Given a model with a set θ of p parameters, the probability of the observable quantities y ₁...N is ρ(y ₁ ... _N|θ). We may treat the set of parameters θ also as a random quantity. Let us denote the prior probability density, i.e., the probability one may assume without knowledge of the data, by π(θ), whereas ρ(θ|y ₁...N), i.e., the density of θ, given the data y ₁...N, may be called the a posteriori density.