Expectation of the description length

Let us define $\mu_i \stackrel{\mathit{def}}{=}E_{\boldsymbol{\tilde{\theta}}}\{\xi_i\}$. Taking expectation over $\boldsymbol{\tilde{\theta}}$ from equation 4 yields  

$$\mu_i(\boldsymbol{\theta}, \boldsymbol{\epsilon_{\boldsymbo... ... E\{f_i(\xi_j \vert j \in \mathcal{J}_i)\} \end{array} \right.$$ (6)

and expectation from equation 5 yields
 $$\begin{multline} L_E(\boldsymbol{\theta}, \boldsymbol{\epsilon_{\boldsymbol{\th... ...on_{\theta_i} + \sum_{t=1}^N \sum_{i \in \mathcal{L_D}} \mu_i(t).\end{multline}$$
We have dropped the subscripts from the expectation operators, but they are always taken over $\boldsymbol{\tilde{\theta}}$.