# Gibbs Sampling

Given a set of documents $$\mathscr{D}$$, each containing terms $$T_d$$, learn a set of "topics" $$\mathscr{T}$$ representative of the "semantic" content of the corpus.

Each topic is characterized by a distribution over terms, $$\phi_t$$. Each document has a latent mixture over topics, $$\theta_d$$.

We want to draw samples from the distribution over our latent random variables, e.g. $$\phi$$, $$\theta$$, and $$T$$. This is very difficult due to the high dimensionality of the event space.

To do this we iteratively examine subsets of our variables and draw from their marginal distribution.