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Yvo Pokern Andrew M. Stuart Petter WibergParameter estimation for partially observed hypoelliptic diffusionsHypoelliptic diffusion processes can be used to model a variety of phenomena in appli- cations 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 inter-sample 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 unob- served solution components, and parameters. Numerical experiments display asymptotic consistency of the method when applied to simulated data. The paper concludes with application of the Gibbs sampler to molecular dynamics data.Bibliographical note: Submitted |