Premium
Parameter estimation for partially observed hypoelliptic diffusions
Author(s) -
Pokern Yvo,
Stuart Andrew M.,
Wiberg Petter
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00689.x
Subject(s) - hypoelliptic operator , consistency (knowledge bases) , limit (mathematics) , mathematics , diffusion , statistical physics , gibbs sampling , work (physics) , estimation theory , statistics , computer science , econometrics , mathematical optimization , partial differential equation , mathematical analysis , physics , thermodynamics , method of characteristics , geometry , bayesian probability
Summary. 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 Δ t and large total observation times N Δ 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.