$$\frac{p(\mathscr M_1|y)}{ p(\mathscr M_2|y) } = \frac{p(\mathscr M_1)}{ p(\mathscr M_2) }\frac{p(y|\mathscr M_1)}{ p(y|\mathscr M_2) }$$

Bayes factor

$$\mathrm{BF_{12}} = \frac{m(y|\mathscr M_1)}{m(y|\mathscr M_2)}$$

• $\mathrm{BF_{12}}$: how many time more likely is model $\mathscr M_1$ than $\mathscr M_2$.

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