Definition: Flat, hard and soft prior distribution
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Prior distributions ▷ Flat vs. hard vs. soft
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Metadata: ID: D116  shortcut: priorflat  author: JoramSoch  date: 20201202, 17:04.
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 nonzero and finite.
 Friston et al. (2002): "Classical and Bayesian Inference in Neuroimaging: Theory"; in: NeuroImage, vol. 16, iss. 2, pp. 465483, 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. 484512, fn. 10; URL: https://www.sciencedirect.com/science/article/pii/S1053811902910918; DOI: 10.1006/nimg.2002.1091.
Metadata: ID: D116  shortcut: priorflat  author: JoramSoch  date: 20201202, 17:04.