Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs
By Yvo Pokern, Andrew M. Stuart, J. H. Zanten. 2012
57 citations recorded by the source corpus.
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.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/31c9b9628f2f1670551bce3d6dde5bd04844e518
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In Finance
In Statistics and Probability
- Kolyan Ray
- Richard Nickl
- Judith Rousseau
- I. Castillo
- Evarist Gin'e
- Botond Szab'o
- D. Chetverikov
- Sara A. van de Geer
Citations in the corpus
- Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions (2018, methodology): “The periodic model (which has also been used in [38, 54] when d = 1) is convenient in our context as it effectively confines the diffusion process (Xt) to a bounded state space T d.”