Question about the joint posterior

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Hi,
In paper section "Computing the Joint Posterior", you define the joint posterior $q(z|\overline{\bf{x}})={\bf{\Pi}} q(z_v|x_v) p(z)$. Here why you also multiply $p(z)$ in the joint posterior, but don't use $q(z|\overline{\bf{x}})={\bf{\Pi}} q(z_v|x_v)$ , which is the product of multiple posteriors?