Index: The Book of Statistical ProofsModel Selection ▷ Bayesian model selection ▷ Family evidence ▷ Log family evidence

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:

\[\label{eq:lfe} \mathrm{LFE}(f) = \log p(y|f) = \log \sum_{i=1}^M p(y|m_i) \, p(m_i|f) \; .\]

Metadata: ID: D80 | shortcut: lfe | author: JoramSoch | date: 2020-07-13, 22:31.