UCL logo

UCL Discovery

UCL home » Library Services » Electronic resources » UCL Discovery

Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs

Pokern, Y; Stuart, AM; van Zanten, JH; (2013) Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs. Stochastic Processes and their Applications , 123 (2) 603 - 628. 10.1016/j.spa.2012.08.010.

Full text not available from this repository.

Abstract

We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian prior with precision operator of differential form, we show that the posterior is also Gaussian with the precision operator also of differential form. The resulting expressions are explicit and lead to algorithms which are readily implementable. Using new functional limit theorems for the local time of diffusions on the circle, we bound the rate at which the posterior contracts around the true drift function.

Type:Article
Title:Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs
DOI:10.1016/j.spa.2012.08.010
Publisher version:http://dx.doi.org/10.1016/j.spa.2012.08.010
Language:English
Keywords:Stochastic differential equation, Nonparametric Bayesian estimation, Posterior consistency
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

Archive Staff Only: edit this record