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Journal Articles Stochastic Systems Year : 2016

Convergence Properties of Weighted Particle Islands with Application to the Double Bootstrap Algorithm

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Abstract

Particle island models [32] provide a means of parallelization of sequential Monte Carlo methods, and in this paper we present novel convergence results for algorithms of this sort. In particular we establish a central limit theorem—as the number of islands and the common size of the islands tend jointly to infinity—of the double boot-strap algorithm with possibly adaptive selection on the island level. For this purpose we introduce a notion of archipelagos of weighted islands and find conditions under which a set of convergence properties are preserved by different operations on such archipelagos. This theory allows arbitrary compositions of these operations to be straightforwardly analyzed, providing a very flexible framework covering the double bootstrap algorithm as a special case. Finally, we establish the long-term numerical stability of the double bootstrap algorithm by bounding its asymptotic variance under weak and easily checked assumptions satisfied typically for models with non-compact state space.

Dates and versions

hal-01593885 , version 1 (27-09-2017)

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Cite

Pierre del Moral, Eric Moulines, Jimmy Olsson, Christelle Vergé. Convergence Properties of Weighted Particle Islands with Application to the Double Bootstrap Algorithm. Stochastic Systems, 2016, 6 (2), pp.367 - 419. ⟨10.1287/15-SSY190⟩. ⟨hal-01593885⟩
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