**I** came across a curio today while looking at recent postings on arXiv, namely a different proof of the convergence of the Data Augmentation algorithm, more than twenty years after it was proposed by Martin Tanner and Wing Hung Wong in a 1987 JASA paper… The convergence under the positivity condition is of course a direct consequence of the ergodic theorem, as shown for instance by Tierney (1994), but the note by Yaming Yu uses instead a Kullback divergence

and shows as Liu, Wong and Kong do for the variance (Biometrika, 1994) that this divergence is monotonically decreasing in *t*. The proof is interesting in that only functional (i.e., non-ergodic) arguments are used, even though I am a wee surprised at ** IEEE Transactions on Information Theory** publishing this type of arcane mathematics… Note that the above divergence is the “wrong” one in that it measures the divergence from , not from . The convergence thus involves a sequence of divergences rather than a single one. (Of course, this has no consequence on the corollary that the total variation distance goes to zero.)