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Random-weight particle filtering of continuous time processes
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Fearnhead, Paul, Papaspiliopoulos, Omiros, Roberts, Gareth O. and Stuart, A. M. (2010) Random-weight particle filtering of continuous time processes. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol.72 (No.4). pp. 497-512. doi:10.1111/j.1467-9868.2010.00744.x ISSN 1369-7412.
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Official URL: http://dx.doi.org/10.1111/j.1467-9868.2010.00744.x
Abstract
It is possible to implement importance sampling, and particle filter algorithms, where the importance sampling weight is random. Such random-weight algorithms have been shown to be efficient for inference for a class of diffusion models, as they enable inference without any (time discretization) approximation of the underlying diffusion model. One difficulty of implementing such random-weight algorithms is the requirement to have weights that are positive with probability 1. We show how Wald's identity for martingales can be used to ensure positive weights. We apply this idea to analysis of diffusion models from high frequency data. For a class of diffusion models we show how to implement a particle filter, which uses all the information in the data, but whose computational cost is independent of the frequency of the data. We use the Wald identity to implement a random-weight particle filter for these models which avoids time discretization error.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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Journal or Publication Title: | Journal of the Royal Statistical Society Series B: Statistical Methodology | ||||
Publisher: | Wiley-Blackwell Publishing, Inc | ||||
ISSN: | 1369-7412 | ||||
Official Date: | September 2010 | ||||
Dates: |
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Volume: | Vol.72 | ||||
Number: | No.4 | ||||
Number of Pages: | 16 | ||||
Page Range: | pp. 497-512 | ||||
DOI: | 10.1111/j.1467-9868.2010.00744.x | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Spanish Government | ||||
Grant number: | MTM2008-06660 |
Data sourced from Thomson Reuters' Web of Knowledge
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