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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper describes a Bayesian model for online learning in the context of random forests models for supervised classification. The main contribution of the paper is the formulation of a novel prior on binary rooted trees that relies on the Mondrian process. An additional novelty of the paper is the use of hierarchical normalized stable processes as priors for the probabilities of the different classes at each terminal node. The paper is well written and the formulation novel.