Equation 7.9: conditioning the expectation on data D or on model M for marginal likelihood?

[maremita]

[Version: 2023-04-01]

In equation 7.9 (page 340) $\mathbb{E}\left[ g(\boldsymbol{\theta})|\mathcal{D} \right]$ should be $\mathbb{E}\left[ g(\boldsymbol{\theta})|M \right]$?

Thanks.

[maremita]

In Martin et al. 2020, the marginal likelihood of the model $\mathcal{M}$, $p(\boldsymbol{y}|\mathcal{M})$, is given by the Equation (5): $$\mathbb{E}\left[ g(\boldsymbol{\theta}) | \mathcal{M} \right] = \int_{\boldsymbol{\Theta}} g(\boldsymbol{\theta}) p(\boldsymbol{\theta} | \mathcal{M}) \texttt{d}\boldsymbol{\theta},$$ wrt the prior $p(\boldsymbol{\theta} | \mathcal{M})$. $\boldsymbol{y}$ is the observed data ($\mathcal{D}$ in the book) and $g(\boldsymbol{\theta}) = p(\boldsymbol{y} | \boldsymbol{\theta}, \mathcal{M}) $.

[murphyk]

Yes, good catch! Fixed.