Definition: Empirical and theoretical prior distribution
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Prior distributions ▷ Empirical vs. nonempirical
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Metadata: ID: D119  shortcut: prioremp  author: JoramSoch  date: 20201202, 17:37.
Definition: Let $p(\theta \vert m)$ be a prior distribution for the parameter $\theta$ of a generative model $m$. Then,

the distribution is called an “empirical prior”, if it has been derived from empirical data;

the distribution is called a “theoretical prior”, if it was specified without regard to empirical data.
 Soch J, Allefeld C, Haynes JD (2016): "How to avoid mismodelling in GLMbased fMRI data analysis: crossvalidated Bayesian model selection"; in: NeuroImage, vol. 141, pp. 469489, eq. 13, p. 473; URL: https://www.sciencedirect.com/science/article/pii/S1053811916303615; DOI: 10.1016/j.neuroimage.2016.07.047.
Metadata: ID: D119  shortcut: prioremp  author: JoramSoch  date: 20201202, 17:37.