Index: The Book of Statistical ProofsModel Selection ▷ Bayesian model selection ▷ Bayes factor ▷ 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 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:

\[\label{eq:lbf} \mathrm{LBF}_{12} = \log \mathrm{BF}_{12} = \log \frac{p(y|m_1)}{p(y|m_2)} \; .\]

Metadata: ID: D84 | shortcut: lbf | author: JoramSoch | date: 2020-07-22, 07:02.