This is the core MCMC sampler for the Dirichlet Process Variable Clustering model described in

Konstantina Palla, David A. Knowles and Zoubin Ghahramani. A nonparametric variable clustering model. NIPS 2012.

PDF here: http://papers.nips.cc/paper/4579-a-nonparametric-variable-clustering-model

Factor analysis models effectively summarise the covariance structure of high dimensional data, but the solutions are typically hard to interpret. This motivates attempting to find a disjoint partition, i.e. a simple clustering, of observed variables into highly correlated subsets. We introduce a Bayesian non-parametric approach to this problem, and demonstrate advantages over heuristic methods proposed to date. Our Dirichlet process variable clustering (DPVC) model can discover block-diagonal covariance structures in data. We evaluate our method on both synthetic and gene expression analysis problems.