Definition: Maximum-a-posteriori estimation

Index: The Book of Statistical Proofs ▷ General 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 $\theta$:

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

 

Sources:

• Wikipedia (2023): "Maximum a posteriori estimation"; in: Wikipedia, the free encyclopedia, retrieved on 2023-12-01; URL: https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation#Description.

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