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I would like to implement a BUGS/WINBUGS or JAGS model that specifies the likelihood node by marginalizing over two parameters. Is this feasible in BUGS/WINBUGS or JAGS?

This is the posterior \begin{align} &P\left( g_{x} , g_{y} | \mathbf{a}\right) \propto P\left( \mathbf{a} | g_{x} , g_{y}\right) P\left( g_{x} , g_{y}\right) \end{align} and here is the likelihood \begin{align} &P\left( \mathbf{a} | g_{x} , g_{y}\right) = \int_{\boldsymbol{\omega}_{R}}\int_{\boldsymbol{\omega}_{T}}P\left( \mathbf{a} | g_{x} , g_{y} , \boldsymbol{\omega}_{R} , \boldsymbol{\omega}_{T}\right)P\left( \boldsymbol{\omega}_{R}\right) P\left( \boldsymbol{\omega}_{T}\right)\mathrm{d}\boldsymbol{\omega}_{R} \mathrm{d}\boldsymbol{\omega}_{T} \end{align} where \begin{align} \boldsymbol{\omega}_{R} \\ \boldsymbol{\omega}_{T} \\ g_{x}\\ g_{y} \\ \end{align} are all stochastic nodes

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