“…A number of authors have attempted to weaken and generalize the original strong assumptions; see e.g., Bédard (2007Bédard ( , 2008, Bédard and Rosenthal (2008), Beskos et al (2009), andSherlock and. Corresponding results have been developed for Langevin MCMC algorithms (Roberts and Rosenthal, 1998), and for simulated tempering algorithms (Atchadé et al, 2011;Roberts and Rosenthal, 2013).…”