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On the convergence of adaptive sequential Monte Carlo methods. (English) Zbl 1342.82127

The paper studies the consistency and fluctuation properties of a class of adaptive sequential Monte Carlo algorithms. A weak law of large numbers is established such that one can consistently approximate normalizing constants. Central limit theorems are proved to hold at the usual Monte Carlo rate and explicit recursion equations are given for the asymptotic variances. This implies that the fluctuation analysis of the limiting algorithm can be used to describe the asymptotic properties of the adaptive algorithm. The efficiency of the algorithm is illustrated by a numerical application with a complex high-dimensional posterior distribution associated with the Navier-Stokes model.

MSC:

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F99 Limit theorems in probability theory
62F15 Bayesian inference
65C05 Monte Carlo methods
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