# Definition: Prior distribution

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

**Definition:** Consider measured data $y$ and some unknown latent parameters $\theta$. A distribution of $\theta$ unconditional on $y$ is called a prior distribution:

The parameters $\lambda$ of this distribution are called the prior hyperparameters and the probability density function is called the prior density:

\[\label{eq:prior-pdf} p(\theta|m) = \mathcal{D}(\theta; \lambda) \; .\]

**Sources:**

**Metadata:**ID: D29 | shortcut: prior | author: JoramSoch | date: 2020-03-03, 16:09.