Definition: Likelihood function

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Likelihood theory ▷ Likelihood function

Definition: Let there be a generative model $m$ describing measured data $y$ using model parameters $\theta$. Then, the probability density function of the distribution of $y$ given $\theta$ is called the likelihood function of $m$:

\[\label{eq:lf} \mathcal{L}_m(\theta) = p(y|\theta,m) = \mathcal{D}(y; \theta) \; .\]

 

Sources:

• original work

Metadata: ID: D28 | shortcut: lf | author: JoramSoch | date: 2020-03-03, 15:50.