In the collapsed Gibbs sampling version of LDA, the posterior distribution of topic assignments for each word is sampled. From what I have read (e.g. http://people.cs.umass.edu/~wallach/courses/s11/cmpsci791ss/readings/griffiths02gibbs.pdf) it looks like people just implement the Gibbs sampling procedure by letting it run until we are sure that we are sampling from the posterior then take the last sample as a good topic assignment.
But shouldn't we be a bit more rigorous than this? For example, what if the sample we take happens to be from a part of the posterior with low probability (this would be unlikely but possible)? Wouldn't it be better to do something like take a Bayes estimator (or average, or mode) of the samples to make sure that we are using a topic assignment that is actually likely?