Understanding the derivation of an equation in LDA modeling When reading the derivation of LDA models, I usually get the following equations.

I do not quite understand the second step, where $p(\mathbf{z}_{-i},\mathbf{w}|\alpha,\beta)$ was removed. Is that because it can be thought of as a constant when studying $z_{i}$. I know this is a common practice in Bayesian statistics, but I am not sure whether $p(\mathbf{z}_{-i},\mathbf{w}|\alpha,\beta)$ is a constant.
 A: Actually it was not "removed", the  symbol does not mean equal! It means that the equation is proportional to the other.
The denominator of the function is used to normalize the value and obtain a distribution in the range [0,1].
For this reason the two equations are proportional, and differ only for a scale factor.
A: Here is the part that explains answer to your question.

Above image is part of complete derivation here:
http://lingpipe-blog.com/2010/07/13/collapsed-gibbs-sampling-for-lda-bayesian-naive-bayes/
p.s. thanks to original author for the paper. I'm just posting it here if it helps in answering the question.
A: I would only further suggest that the OP consider the simple case of Bayes' rule which gets applied all over the place in these derivations and from which the question posed comes from. You're looking at the denominator which indeed is just a normalization constant that is the same across any value z_i for which you may ask the probability of given the latent variables and parameters. So your equations are simply proportional to each other. 
I think another important thing to note is that often this denominator is impossible to calculate or work with efficiently, I think that becomes more apparent when you think of what it would take to calculate the probability p(z_-i,w|a,b): this refers to the probability of one latent variable value and one set of words (if I remember correctly), and there are many combinations of them (z*w ?)
