Index: The Book of Statistical ProofsGeneral Theorems ▷ Bayesian statistics ▷ Probabilistic modeling ▷ Marginal likelihood

Definition: Let there be a generative model $m$ describing measured data $y$ using model parameters $\theta$ and a prior distribution on $\theta$. Then, the marginal probability density function of $y$ across the parameter space $\Theta$ is called the marginal likelihood:

\[\label{eq:ml} p(y|m) = \int_{\Theta} p(y|\theta,m) \, p(\theta|m) \, \mathrm{d}\theta \; .\]
 
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Metadata: ID: D33 | shortcut: ml | author: JoramSoch | date: 2020-03-03, 16:49.