Definition: Log family evidence
Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Family evidence ▷ Log family evidence
Sources:
Metadata: ID: D80 | shortcut: lfe | author: JoramSoch | date: 2020-07-13, 22:31.
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 log family evidence is given by the logarithm of the family evidence:
\[\label{eq:lfe} \mathrm{LFE}(f) = \log p(y|f) = \log \sum_{i=1}^M p(y|m_i) \, p(m_i|f) \; .\]- 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: D80 | shortcut: lfe | author: JoramSoch | date: 2020-07-13, 22:31.