This week we discussed how to apply a Dirichlet process-based method to real problems. We focused on the Infinite Gaussian Mixture Model and its uses in spike sorting (Wood & Black, 2008). In this model, the observed data come from an unknown (and potentially infinite) number of multivariate Gaussians. Our goal is to cluster the observations that come from the same Gaussian. This requires an MCMC approach. We chose to examine a collapsed Gibbs sampler which takes advantage of conjugate priors (the inverse Wishart for the multivariate normal). Combined with last week’s results on exchangeability, a Gibbs sweep merely needed to examine each observation given the current labeling of all other observations. The prior for the clustering was the given by the Chinese Restaurant Process and the likelihood became a multivariate Student-t. Next week, we will see how sample over the hyperparameter for the CRP.