Definition: Posterior distribution
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Probabilistic modeling ▷ Posterior distribution
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Metadata: ID: D32 | shortcut: post | author: JoramSoch | date: 2020-03-03, 16:43.
Definition: Consider measured data $y$ and some unknown latent parameters $\theta$. The distribution of $\theta$ conditional on $y$ is called the posterior distribution:
\[\label{eq:post} \theta|y \sim \mathcal{D}(\phi) \; .\]The parameters $\phi$ of this distribution are called the posterior hyperparameters and the probability density function is called the posterior density:
\[\label{eq:prior-pdf} p(\theta|y,m) = \mathcal{D}(\theta; \phi) \; .\]Metadata: ID: D32 | shortcut: post | author: JoramSoch | date: 2020-03-03, 16:43.