Abstract

Co-authors: Christelle Vergé, Pierre Del Moral, and Eric Moulines

This talk discusses parallelisation of sequential Monte Carlo methods via the particle island framework (Vergé et al., 2013) and presents some novel convergence results for methods of this sort. More specifically, we introduce the concept of weighted archipelagos (i.e. sets of weighted particle islands, where each island is itself a weighted sample of particles) and define three different operations on such archipelagos, namely: selection on the island level, selection on the particle level, and mutation. We then establish that these operations preserve a set of convergence properties, including asymptotic normality, of the archipelago as the number of islands as well as the number of particles of each island tend jointly to infinity. Moreover, we provide recursive formulas for the asymptotic variance associated with each operation. As our results allow arbitrary compositions of the mentioned operations to be analysed, we may use the same for establishing the convergence properties of not only the double bootstrap algorithm but also generalisations of this algorithm.