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March 2014 Error bounds and normalising constants for sequential Monte Carlo samplers in high dimensions
Alexandros Beskos, Dan O. Crisan, Ajay Jasra, Nick Whiteley
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Adv. in Appl. Probab. 46(1): 279-306 (March 2014). DOI: 10.1239/aap/1396360114

Abstract

In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. The SMC samplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density in d dimensions our results are concerned with d → ∞, while the number of Monte Carlo samples, N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative L2-error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd2).

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Alexandros Beskos. Dan O. Crisan. Ajay Jasra. Nick Whiteley. "Error bounds and normalising constants for sequential Monte Carlo samplers in high dimensions." Adv. in Appl. Probab. 46 (1) 279 - 306, March 2014. https://doi.org/10.1239/aap/1396360114

Information

Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 1291.65009
MathSciNet: MR3189059
Digital Object Identifier: 10.1239/aap/1396360114

Subjects:
Primary: 65C05
Secondary: 62F15

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 1 • March 2014
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