2007/10/29 by Yvo Pokern, Y. Pokern, A. M. Stuart +6 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #FOS: Computer and information sciences #Methodology (stat.ME) #Model Reduction and Neural Networks #Statistical and numerical algorithms #stat.ME
paper · pdf · doi:10.48550/arxiv.0710.5442
26 pages, submitted to JRSS(B)
openalex publication_date 2007/10/29 · arxiv created 2007/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 inter-sample times Δt and large total observation times NΔt. 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 application of the Gibbs sampler to molecular dynamics data.