Outline:

Sequential Monte Carlo (SMC) methods form a powerful and flexible class of computational algorithms for approximating (sequences of) intractable integrals. Lindsten et al. (2016+) introduce an extension of this family
which uses an iterative decomposition strategy to break the problem up into more manageable subproblems which can themselves be addressed with SMC techniques; it allows computational effort to be adaptively focussed on difficult subproblems and shows promising performance. There are numerous interesting theoretical and practical questions related to this class of methods: obtaining a central limit theorem; developing strategies for the efficient deployment of these techniques in real problems and addressing some real problems arising, for example, in the context of phylogenetic trees.

References:

F. Lindsten, A. M. Johansen, C. Naesseth, B. Kirkpatrick, T. Schön, J. A. D. Aston, and A. Bouchard-Côté (2016+). Divide and conquer with sequential Monte Carlo. To appear in /Journal of Computational and Graphical Statistics/. Available as: arxiv 1406.4993.