A clever way to derive the collapsed Gibbs sampling for LDA

Inspired by Tom Griffiths technical report, Gibbs Sampling in the Generative Model of Latent Dirichlet Allocation, I derive the collapsed Gibbs sampling for LDA by myself using the tricks in Tom's report. These tricks are universally applicable to other topic models:

• simplify the conditional property by employing Bayes theorem and
  d-separation property
• derive the results of conditional probability directly from the result of
  the predictive likelihood of Dirichlet/multinomial distribution
  

There is no lengthy and complex computation like those in Wang Yi's note or Gregor Heinrich's note. It is easy to understand and has intuitive explanation for the formulas involved. I wrote up a report for my derivation, as a complementary to Tom's note:
Derivation of Collapsed Gibbs Sampling for LDA