y

observed data $y_1,\cdots ,y_n$

$M_i$

candidate model

${\theta }_i$

vector of parameters in the model

$g\left({\theta }_i\right)$

the prior density of the parameters ${\theta }_i$

$P\left(y\mathrm{<mo>\; |\; </mo>}{M}_i\right)$

marginal likelihood

$f\left(y\mathrm{<mo>\; |\; </mo>}{\theta }_i\right)$

the density of the data given

$L\left({\theta }_i\mathrm{<mo>\; |\; </mo>}y\right)$

the likelihood of y given the model $M_i$