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Parameter estimation for partially observed hypoelliptic diffusions
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Pokern, Yvo, Stuart, A. M. and Wiberg, Petter (2009) Parameter estimation for partially observed hypoelliptic diffusions. Royal Statistical Society. Journal. Series B: Statistical Methodology, Vol.71 (No.1). pp. 49-73. doi:10.1111/j.1467-9868.2008.00689.x
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Official URL: http://dx.doi.org/10.1111/j.1467-9868.2008.00689.x
Abstract
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact likelihoods for the transition densities are typically not known, approximations are used that are expected to work well in the limit of small intersample times Delta t and large total observation times N Delta t. Hypoellipticity together with partial observation leads to ill conditioning requiring a judicious combination of approximate likelihoods for the various parameters to be estimated. We combine these in a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters. Numerical experiments illustrate asymptotic consistency of the method when applied to simulated data. The paper concludes with an application of the Gibbs sampler to molecular dynamics data.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Royal Statistical Society. Journal. Series B: Statistical Methodology | ||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | ||||
| ISSN: | 1369-7412 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.71 | ||||
| Number: | No.1 | ||||
| Number of Pages: | 25 | ||||
| Page Range: | pp. 49-73 | ||||
| DOI: | 10.1111/j.1467-9868.2008.00689.x | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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