Review for NeurIPS paper: Replica-Exchange Nos\'e-Hoover Dynamics for Bayesian Learning on Large Datasets

The paper proposes a novel MCMC-type algorithm to perform Bayesian inference on large datasets. The paper is a mixture of replica exchange, Nose-Hoover dynamics and non-standard acceptance criterion to deal with mini-batches. All the reviewers participated actively to the discussion after the rebuttal was made available. Although all the ingredients of the proposed method do exist, their combination is original and potentially useful for the ML literature as pointed out by most reviewers. Theorem 2 is also neat and proposes a nice way to propose swaps between replicas using mini-batches.