The authors develop a novel Markov chain method (ACIMH) that is designed to sample efficiently by adapting to the features of the target distribution, learning from the samples obtained previously. Their approach is based on independence MetropolisHastings (IMH), and takes the proposal distribution to be an estimate of the target distribution. Its appeal is that the efficiency of IMH is controlled by how close the proposal density is to the target density. If a very accurate estimate of the target density can be obtained, then the samples obtained by the Markov chain are nearly independent, leading to near-optimal accuracy of Monte Carlo approximations. The authors’ estimate of the target density is based on D-vine copulas, an extremely flexible class of models that has not been used previously for this purpose. Other authors have proposed similar “adaptive” IMH methods based on alternative estimates of the target density, in particular mixture distributions such as normal or t mixtures (Andrieu and Moulines 2006; Andrieu and Thoms 2008). Continued development of efficient general-purpose sampling algorithms like these is critical as we create robust software packages for Bayesian statistics that will encourage its widespread use. D-vine copulas use a factorization approach that may scale more effectively with dimension than the mixture model approach. ACIMH factorizes the target density as