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This paper proposed the population posterior distribution for Bayesian modeling of streams of data and showed how stochastic optimization could be used to find a good approximation. The proposed framework and algorithm were demonstrated on both latent Dirichlet allocation and Dirichlet process mixture models on text and geolocation data and were shown to perform better than previous work in some cases. Overall, I think the main idea of the paper is very interesting and it would fit in well at NIPS. There are a few aspects of the paper that could use some more discussion though. First, the authors were very careful throughout the paper to use the term "Bayesian modeling", except the title uses "Bayesian inference", which this paper definitely does not provide a method for.