Definition: Flat, hard and soft prior distribution

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Prior distributions ▷ Flat vs. hard vs. soft

Definition: Let $p(\theta \vert m)$ be a prior distribution for the parameter $\theta$ of a generative model $m$. Then,

• the distribution is called a “flat prior”, if its precision is zero or variance is infinite;

• the distribution is called a “hard prior”, if its precision is infinite or variance is zero;

• the distribution is called a “soft prior”, if its precision and variance are non-zero and finite.

 

Sources:

• Friston et al. (2002): "Classical and Bayesian Inference in Neuroimaging: Theory"; in: NeuroImage, vol. 16, iss. 2, pp. 465-483, fn. 1; URL: https://www.sciencedirect.com/science/article/pii/S1053811902910906; DOI: 10.1006/nimg.2002.1090.
• Friston et al. (2002): "Classical and Bayesian Inference in Neuroimaging: Applications"; in: NeuroImage, vol. 16, iss. 2, pp. 484-512, fn. 10; URL: https://www.sciencedirect.com/science/article/pii/S1053811902910918; DOI: 10.1006/nimg.2002.1091.

Metadata: ID: D116 | shortcut: prior-flat | author: JoramSoch | date: 2020-12-02, 17:04.