Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Probabilistic modeling ▷ Prior predictive distribution

Definition: Consider a full probability model with likelihood function $p(y \vert \theta)$ and prior distribution $p(\theta)$. Then, the marginal distribution of any data point $y_{\mathrm{new}}$, accounting for the prior distribution, is called the prior predictive distribution:

\[\label{eq:prior-pred} p(y_{\mathrm{new}}) = \int p(y_{\mathrm{new}} \vert \theta) \, p(\theta) \, \mathrm{d}\theta \; .\]
 
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Metadata: ID: D202 | shortcut: prior-pred | author: aloctavodia | date: 2024-08-19, 14:57.