Definition: Family evidence
Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Family evidence ▷ Definition
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Metadata: ID: D180 | shortcut: fe | author: JoramSoch | date: 2022-10-20, 09:57.
Definition: Let $f$ be a family of $M$ generative models $m_1, \ldots, m_M$, such that the following statement holds true:
\[\label{eq:fam} f \Leftrightarrow m_1 \vee \ldots \vee m_M \; .\]Then, the family evidence (FE) of $f$ is defined as the marginal probability relative to the model evidences $p(y \vert m_i)$, conditional only on $f$:
\[\label{eq:fe} \mathrm{FE}(f) = p(y|f) \; .\]- Soch J, Allefeld C (2018): "MACS – a new SPM toolbox for model assessment, comparison and selection"; in: Journal of Neuroscience Methods, vol. 306, pp. 19-31, eq. 16; URL: https://www.sciencedirect.com/science/article/pii/S0165027018301468; DOI: 10.1016/j.jneumeth.2018.05.017.
Metadata: ID: D180 | shortcut: fe | author: JoramSoch | date: 2022-10-20, 09:57.