Statistics – Methodology
Scientific paper
2012-02-05
Statistics
Methodology
Scientific paper
We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. We rewrite the likelihood in terms of Riemann integrals, by introducing the local time of the process, and specify a centered Gaussian prior on the drift with a precision operator that is of differential form. It is proved that this is a conjugate prior for the likelihood and hence that the posterior is also Gaussian. We give an explicit expression for the posterior precision operator, also of differential form, and show that the posterior mean is the solution of a differential equation requiring inversion of the posterior precision for its solution. Moreover, we bound the rate at which the posterior contracts around the true drift function. Our formulation of the estimation problem leads to algorithms which are readily implementable and analyzed using ideas from the numerical analysis of differential equations. The central results proved here require tools from the analysis of differential equations, together with new functional limit theorems for the local time of diffusions on the circle.
Pokern Y.
Stuart Andrew M.
van Zanten J. H.
No associations
LandOfFree
Posterior Consistency via Precision Operators for Bayesian Nonparametric Drift Estimation in SDEs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Posterior Consistency via Precision Operators for Bayesian Nonparametric Drift Estimation in SDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Posterior Consistency via Precision Operators for Bayesian Nonparametric Drift Estimation in SDEs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-461793