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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This is an interesting and well written paper using variational approximations to deal with non-Gaussian likelihoods. The ideas in the paper are very well explained and the connections to the existing literature are good. The connections to the EKF and UKF are interesting. In section 1 and in section 3, it is claimed that the proposed methodology would be applicable to problems with non-factorizing likelihoods, but no further details are provided about this, and no experiments deal with this case.