Advances in Applied Probability

Error bounds and normalising constants for sequential Monte Carlo samplers in high dimensions

Alexandros Beskos, Dan O. Crisan, Ajay Jasra, and Nick Whiteley

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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).

Article information

Source
Adv. in Appl. Probab. Volume 46, Number 1 (2014), 279-306.

Dates
First available in Project Euclid: 1 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1396360114

Digital Object Identifier
doi:10.1239/aap/1396360114

Mathematical Reviews number (MathSciNet)
MR3189059

Zentralblatt MATH identifier
1291.65009

Subjects
Primary: 65C05: Monte Carlo methods
Secondary: 62F15: Bayesian inference

Keywords
Sequential Monte Carlo high dimensions propagation of chaos normalising constant

Citation

Beskos, Alexandros; Crisan, Dan O.; Jasra, Ajay; Whiteley, Nick. Error bounds and normalising constants for sequential Monte Carlo samplers in high dimensions. Adv. in Appl. Probab. 46 (2014), no. 1, 279--306. doi:10.1239/aap/1396360114. https://projecteuclid.org/euclid.aap/1396360114


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