= Solution
Evaluate <Bayes' theorem> at the <posterior mode> $\mu$:
$$
p(\mathcal D)=\frac{p(\mathcal D\mid\mu)p(\mu)}{p(\mu\mid\mathcal D)}.
$$
The <multivariate normal density> in the <Laplace approximation> has height $(2\pi)^{-d/2}|\Sigma|^{-1/2}$ at its <mean>. Therefore
$$
\boxed{p(\mathcal D)\simeq p(\mathcal D\mid\mu)p(\mu)(2\pi)^{d/2}|\Sigma|^{1/2}}.
$$
Equivalently, the approximate log <marginal likelihood> is
$$
\boxed{\log p(\mathcal D)\simeq\log p(\mathcal D\mid\mu)+\log p(\mu)+\frac d2\log(2\pi)+\frac12\log|\Sigma|}.
$$
The <determinant> factor accounts for the volume of the locally plausible parameter region, which the peak <likelihood> alone does not measure.
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