2014/10/15 by Pierre Del Moral, Del Moral, Pierre, Éric Moulines +5
Mathematics · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Statistics Theory (math.ST) #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.1410.4231
openalex publication_date 2014/10/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Particle island models (Vergé et al., 2013) 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 bootstrap 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 for a wide range of models with possibly non-compact state space.