Fabian Wagner, Iason Papaioannou, Elisabeth Ullmann and I have deposited a new manuscript in the arXiv: “Multilevel Sequential Importance Sampling for Rare Event Estimation”. In this manuscript, we essentially work towards employing the Multilevel Sequential² Monte Carlo framework for the estimation of rare events rather than Bayesian inversion; see (2018, J. Comput. Phys. 368, p. 154-178). Then, we show in numerical experiments that this approach is reasonable and that it can outperform single level strategies. Moreover, the approach solves nestedness issues that can occur in Subset Simulation algorithms. Last, I want to mention that we consider MCMC algorithms that are based on adaptive von Mises-Fischer-Nakagami proposals. Those appear to be especially useful in the mutation step in Sequential Monte Carlo methods. For more information, please have a look at the article.