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

Definition: Let $m_0$ and $m_1$ be two generative models describing the same measured data $y$ using different model parameters $\theta_0 \in \Theta_0$ and $\theta_1 \in \Theta_1$. Then, the quotient of the maximized likelihood functions of these two models is denoted as $\Lambda_{01}$ and is called the likelihood ratio of $m_0$ relative to $m_1$:

\[\label{eq:lr} \Lambda_{01} = \frac{\operatorname*{max}_{\theta_0 \in \Theta_0} \mathcal{L}_{m_0}(\theta_0)}{\operatorname*{max}_{\theta_1 \in \Theta_1} \mathcal{L}_{m_1}(\theta_1)} = \frac{p(y|\hat{\theta}_0,m_0)}{p(y|\hat{\theta}_1,m_1)} \; .\]
 
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Metadata: ID: D198 | shortcut: lr | author: JoramSoch | date: 2024-06-14, 14:44.