# #StackBounty: #bayesian #kullback-leibler #variational-bayes #approximate-inference #variational Estimating the posterior distributions…

### Bounty: 100

In the following graphical model

the generative model of the mixture of the gamma distribution is given as
$$begin{equation} begin{split} p(z|pi)&=prod_{k=1}^Kpi_k^{z_k}\ p(gamma|z)&=prod_{k=1}^Kmathrm{Gamma}(gamma|a,b)^{z_k} end{split} end{equation}$$
so the joint distribution of $$boldsymbol{gamma}$$ and $$mathrm{z}$$ is
$$p(boldsymbol{gamma},mathrm{z}|pi,a,b)=prod_{i=1}^Nprod_{k=1}^Kpi_k^{z_{ik}}mathrm{Gamma}(gamma_i|a,b)^{z_{ik}}$$
How can I use variational message passing to compute messages from $$pi$$, $$a$$, $$b$$ and $$z$$ ?

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