\begin{equation}
(d_{xt} \mid \overline{m}_{xt}) \stackrel{\mbox{\scriptsize ind}}{\sim} \mbox{Poisson}(\textsc{e}_{xt}\overline{m}_{xt}), \quad \mbox{with} \quad (\log \overline{m}_{xt} \mid f_{t}(x)) \stackrel{\mbox{\scriptsize ind}}{\sim} \mbox{N}(f_{t}(x), \sigma_{\overline{m}}^2),
\label{eq1}
\end{equation}
