Error bounds and normalising constants for sequential monte carlo samplers in high dimensions.
Advances in Applied Probability
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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. TheSMCsamplers 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 theSMCsampler 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). © Applied Probability Trust 2014.
|Title:||Error bounds and normalising constants for sequential monte carlo samplers in high dimensions|
|Open access status:||An open access version is available from UCL Discovery|
|Additional information:||Published in Advances in Applied Probability, 46 (1). Copyright (c) Applied Probability Trust 2014.|
|Keywords:||High dimensions, Normalising constant, Propagation of chaos, Sequential Monte Carlo|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science
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