As long-time enthusiast for auxiliary variables methods in Bayesian MCMC, we are glad to have the opportunity to discuss this interesting paper.The authors have a reputation for picturesque and metaphorical titles, and this paper is no exception. We were intrigued by the 'artistic' aspirations here, but remain in some doubt as to whether this should be read in the sense of 'non-scientific' or 'aesthetically pleasing'! One of the objectives in preparing our discussion was to see whether trying to relate the ideas here more closely to existing auxiliary variables methods might both diminish the former characteristic and enhance the latter. This was only partially successful: is our intention doomed, and can the authors do better?
