The transcoding sampler for stick-breaking inferences on Dirichlet process mixtures

An issue of Dirichlet process mixture models is the slow mixing of the MCMC posterior chain produced by conditional Gibbs samplers based on its stick-breaking representation, as opposed to marginal collapsed Gibbs samplers based on the Polya urn, which have smaller integrated autocorrelation times. We solve the issue by introducing the transcoding sampler, a new stick-breaking sampler which, conditional to the exchangeable partition posterior produced by any other sampler, enriches it with posterior samples of the stick-breaking parameters. This new sampler is therefore able to match the autocorrelation times of any other sampler, including marginal collapsed Gibbs samplers; it outperforms the slice sampler and removes the need to accelerate it with label-switching Metropolis jumps. As a building block for the transcoding sampler we develop the i.i.d. transcoding algorithm which, conditional to a posterior partition of the data, can infer back which specific stick in the stick-breaking construction each observation originated from.