PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Nonparametric Bayesian drift estimation for one-dimensional diffusion processes
Yvo Pokern, Omiros Papaspiliopoulos, Gareth Roberts and Andrew Stuart
Bernoulli 2009.

Abstract

We consider diffusions on the circle and establish a Bayesian estimator for the drift function based on observing the local time and using Gaussian priors. Given a standard Girsanov likelihood, we prove that the procedure is well-defined and that the posterior enjoys robustness against small deviations of the local time. A simple method for estimating the local time from high-frequency discrete time observations yielding control of the $L^2$ error is proposed. Complemented by a finite element implementation this enables error-control for a fixed random sample all the way from high-frequency discrete observation to the numerical computation of the posterior mean and covariance. An empirical Bayes procedure is suggested which allows automatic selection of the smoothness of the prior in a given family. Some numerical experiments extend our observations to subsets of the real line other than circles and exhibit more probabilistic convergence properties such as rates of posterior contraction.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:6820
Deposited By:Omiros Papaspiliopoulos
Deposited On:08 March 2010