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Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions

Part of: Parametric inference Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  22 February 2016

Alexandros Beskos ,
Dan O. Crisan ,
Ajay Jasra  and
Nick Whiteley
Alexandros Beskos*
Affiliation:
National University of Singapore
Dan O. Crisan*
Affiliation:
Imperial College London
Ajay Jasra*
Affiliation:
National University of Singapore
Nick Whiteley*
Affiliation:
University of Bristol
*
∗ Postal address: Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, 117546, Singapore.
∗∗ Postal address: Department of Mathematics, Imperial College London, 180 Queens Gate, London SW7 2AZ, UK.
∗ Postal address: Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, 117546, Singapore.
∗∗∗∗ Postal address: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
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Abstract

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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 -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).

Keywords

Sequential Monte Carlohigh dimensionspropagation of chaosnormalising constant

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 62F15: Bayesian inference
Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 279 - 306
Copyright
© Applied Probability Trust 

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