Category:Bayes' Factors
This category contains results about Bayes' Factors.
Definitions specific to this category can be found in Definitions/Bayes' Factors.
Let $D$ be a set of data which may be assumed to have arisen from one of only $2$ possible models: $M_1$ or $M_2$.
Let the prior probabilities of $M_1$ and $M_2$ be denoted $\map \Pr {M_1}$ and $\map \Pr {M_2}$ such that $\map \Pr {M_2} = 1 - \map \Pr {M_1}$.
Let the posterior probabilities be denoted $\condprob {M_1} D$ and $\condprob {M_2} D$ such that $\condprob {M_2} D = 1 - \condprob {M_1} D$.
From Bayes' Theorem we have: $\dfrac {\condprob {M_1} D} {\condprob {M_2} D} = B_{1 2} \dfrac {\map \Pr {M_1} } {\map \Pr {M_2} }$ such that:
- $B_{1 2} = \dfrac {\condprob D {M_1} } {\condprob D {M_2} }$
The coefficient $B_{1 2}$ is called the Bayes' factor.
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