Global class proportion parameters, $\vec{\pi}$

This is only required for model 1. This is sampled from using Metropolis-Hastings. The following terms are recalculated for each parameter change:

$$\prod_i^N \sum_{k=1}^K \{ \pi_k w_{ik}p(y_i\vert x_i=k,\theta_k)\}$$

$$p(\vec{\pi})$$ (31)