Paper:
A hybrid sampler for Poisson-Kingman mixture models
This paper concerns the introduction of a new Markov Chain Monte Carlo scheme for posterior sampling in Bayesian nonparametric mixture models with priors that belong to the general Poisson-Kingman class. We present a novel compact way of representing the infinite dimensional component of the model such that while explicitly representing this infinite component it has less memory and storage requirements than previous MCMC schemes. We describe comparative simulation results demonstrating the efficacy of the proposed MCMC algorithm against existing marginal and conditional MCMC samplers.

Review:
Summary: The authors present a new MCMC method for a general class of bayesian nonparametric models, namely Poisson-Kingman random probability measures.They describe the class of models, the generative procedure and the insight that yields an mcmc routine for inference, as well as existing methods for the same/similar class of models, namely marginal and conditional samplers. They compare their sampler to standard marginal and conditional samplers, comparing effective sample size and running time.  - QualityThis paper develops an inference method for a very general class of models.It seems technically sound and provides an adequate summary of existing methods and how they relate to the method they present.  - ClarityThis paper isn't that clearly written, which may be due to the page limit.For instance, it is very difficult to decipher the notation in the generative procedure of section 2.1, which is arguably the most important section for appreciating the authors' contribution.  - Originality It is my understanding that a sampler for this general class of models is novel. - Significance If the idea were presented more fluidly, this paper could serve as a nice review and reference for this type of sampler.I think the idea has the potential to be impactful, but may fall short due to presentation.  Comments:- A figure or diagram of your generative process (the stick breaking construction) and how it is distinct from the standard DP stick breaking construction of Ishwaran and James would make section 2 (as well as your methodological contribution in general) easier to understand.