This arXival from last spring/summer by Martino, Elvira, Luengo and Corander combines and extends upon recent advances of Importance Sampling, using mainly ideas from Adaptive Multiple lmportance Sampling (AMIS) and Population Monte Carlo (PMC). The extension consists of the idea to not use the Importance Sampling procedure itself to come up with new proposal distributions, but rather to run a Markov Chain. The output of which is used solely as the location parameter for IS proposal distributions $q_{n,t}$. The weights of the samples drawn from these are Rao-Blackwellized using the deterministic mixture idea of Zhou and Owen, and as far as I can see only the Importance Samples are used for estimating integrands.