Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Bayes factor ▷ Group log Bayes factor

Definition: Let there be two generative models $m_1$ and $m_2$ which are mutually exclusive, but not necessarily collectively exhaustive:

\[\label{eq:m12} \neg (m_1 \land m_2)\]

Then, the group Bayes factor for a group data set $Y = \left\lbrace y_1, \ldots, y_N \right\rbrace$ in favor of $m_1$ and against $m_2$ is the product of the Bayes factors across all units of the group:

\[\label{eq:gbf} \mathrm{GBF}_{12} = \prod_{i=1}^N \frac{p(y_i \vert m_1)}{p(y_i \vert m_2)} \; .\]

The group log Bayes factor is given by the logarithm of the group Bayes factor:

\[\label{eq:glbf} \mathrm{GLBF}_{12} = \log \mathrm{GBF}_{12} = \sum_{i=1}^N \log \frac{p(y_i|m_1)}{p(y_i|m_2)} \; .\]
 
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Metadata: ID: D234 | shortcut: glbf | author: JoramSoch | date: 2026-06-04, 17:32.