Gibbs sampling procedure for GMM

In Rasmussen's paper, there is no description about the Gibbs sampling procedure. I found another paper, Probability density estimation via an infinite Gaussian mixture model: application to statistical process monitoring, which uses the same formulas as Rasmussen, provides a description of an iteration of Gibbs sampling as follows:

1. For i=1:n
   1. sample indicators c
2. update k, the current number of represented (non-empty) clusters
3. for j=1:k
   1. update , the number of data points belonging to cluster j.
   2. update mixture weight
4. update the overall mixture weight for unrepresented mixtures:
5. for j=1:k
   1. sample cluster mean
   2. sample cluster precision
6. update hyper-parameters
   1. sample 
   2. sample
   3. sample
   4. sample
   5. sample
      

The above notations follow the conventions of Rasmussen's paper