Definition: Log Bayes factor
Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Bayes factor ▷ Log Bayes factor
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Metadata: ID: D84 | shortcut: lbf | author: JoramSoch | date: 2020-07-22, 07:02.
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 Bayes factor in favor of $m_1$ and against $m_2$ is the ratio of the model evidences of $m_1$ and $m_2$:
\[\label{eq:bf} \mathrm{BF}_{12} = \frac{p(y|m_1)}{p(y|m_2)} \; .\]The log Bayes factor is given by the logarithm of the Bayes factor:
\[\label{eq:lbf} \mathrm{LBF}_{12} = \log \mathrm{BF}_{12} = \log \frac{p(y|m_1)}{p(y|m_2)} \; .\]- 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. 18; URL: https://www.sciencedirect.com/science/article/pii/S0165027018301468; DOI: 10.1016/j.jneumeth.2018.05.017.
Metadata: ID: D84 | shortcut: lbf | author: JoramSoch | date: 2020-07-22, 07:02.