We induce these variables conditioned on all the observable words in the data set w. Since direct joint sampling from the posterior distributions is intractable, we use Gibbs sampling for approximate inference.
to improve mixing time, we also resample components η k i and η l i when word i has changed event membership from type k to type l. In addition we define classes of closely related words (heuristically based on the covariance matrix) by classifying words as related when their similarity exceeds an empirically determined threshold.