Definition: Posterior predictive distribution
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Bayesian statistics ▷
Probabilistic modeling ▷
Posterior predictive distribution
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Metadata: ID: D201 | shortcut: post-pred | author: aloctavodia | date: 2024-08-18, 07:50.
Definition: Consider a full probability model with likelihood function $p(y \vert \theta)$ and posterior distribution $p(\theta \vert y)$ based on measured data $y$. Then, the marginal distribution of new data $y_{\mathrm{new}}$, predicted based on the posterior distribution, is called the posterior predictive distribution:
\[\label{eq:post-pred} p(y_{\mathrm{new}} \vert y) = \int p(y_{\mathrm{new}} \vert \theta) \, p(\theta \vert y) \, \mathrm{d}\theta \; .\]Metadata: ID: D201 | shortcut: post-pred | author: aloctavodia | date: 2024-08-18, 07:50.