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:

$$\label{eq:prior} \theta \sim \mathcal{D}(\lambda) \; .$$

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:

• original work

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