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Convergence Properties of Weighted Particle Islands with Application to the Double Bootstrap Algorithm
VERGÉ, Christelle
Centre National d'Études Spatiales [Toulouse] [CNES]
ONERA - The French Aerospace Lab [Palaiseau]
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Centre National d'Études Spatiales [Toulouse] [CNES]
ONERA - The French Aerospace Lab [Palaiseau]
Language
en
Article de revue
This item was published in
Stochastic Systems. 2016-12, vol. 6, n° 2, p. 367 - 419
INFORMS Applied Probability Society
English 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 ...Read more >
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.Read less <
Origin
Hal imported