The partition function is given by
$$ \begin{align*} Z_{GB} =& \int \sum_{\tilde{\boldsymbol{h}}}^{\tilde{\boldsymbol{H}}} e^{-\vert\vert\frac{\tilde{\boldsymbol{x}} -\boldsymbol{a}}{2\boldsymbol{\sigma}}\vert\vert^2 + \boldsymbol{b}^T \tilde{\boldsymbol{h}} + (\frac{\tilde{\boldsymbol{x}}}{\boldsymbol{\sigma}^2})^T \boldsymbol{W}\tilde{\boldsymbol{h}}} d\tilde{\boldsymbol{x}} . \end{align*} $$