van Zanten, JH;
Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs.
Stochastic Processes and their Applications
603 - 628.
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.
|Title:||Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs|
|Keywords:||Stochastic differential equation, Nonparametric Bayesian estimation, Posterior consistency|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science|
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