Index: The Book of Statistical ProofsGeneral Theorems ▷ Bayesian statistics ▷ Probabilistic modeling ▷ Maximum-a-posteriori estimation

Definition: Consider a posterior distribution of an unknown parameter $\theta$, given measured data $y$, parametrized by posterior hyperparameters $\phi$:

\[\label{eq:post} \theta|y \sim \mathcal{D}(\phi) \; .\]

Then, the value of $\theta$ at which the posterior density attains its maximum is called the “maximum-a-posteriori estimate”, “MAP estimate” or “posterior mode” of $\theta$:

\[\label{eq:prior-pdf} \hat{\theta}_\mathrm{MAP} = \operatorname*{arg\,max}_\theta \mathcal{D}(\theta; \phi) \; .\]

Metadata: ID: D191 | shortcut: map | author: JoramSoch | date: 2023-12-01, 14:32.