This paper has some strong points and some not so strong points. The main strong point is that using BDMC to assess convergence of MCMC operators is a beautifully simple idea, and easy to implement, which in my opinion means that this work is potentially high impact. This is particularly true in the context of probabilistic programming systems, which indeed are the envisioned use case here, and I think all such systems would do well to at least implement this method. The authors cite an arxiv submission on BDMC as existing work, but (I think wisely) choose to devote a relatively large amount of space to reiterating its description. Unfortunately this does mean that the main technical contributions presented in sections 3.1 and 3.2 are somewhat rushed, and it is unfortunately also here where the writing quality slips a bit.

This paper has some strong points and some not so strong points. The main strong point is that using BDMC to assess convergence of MCMC operators is a beautifully simple idea, and easy to implement, which in my opinion means that this work is potentially high impact. This is particularly true in the context of probabilistic programming systems, which indeed are the envisioned use case here, and I think all such systems would do well to at least implement this method. The authors cite an arxiv submission on BDMC as existing work, but (I think wisely) choose to devote a relatively large amount of space to reiterating its description. Unfortunately this does mean that the main technical contributions presented in sections 3.1 and 3.2 are somewhat rushed, and it is unfortunately also here where the writing quality slips a bit.