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Non parametric Bayesian drift estimation for one-dimensional diffusion processes
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Pokern, Yvo, Papaspiliopoulos, Omiros, Roberts, Gareth O. and Stuart, A. M. (2009) Non parametric Bayesian drift estimation for one-dimensional diffusion processes. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.29).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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 L2 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.
Item Type: | Working or Discussion Paper (Working Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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Library of Congress Subject Headings (LCSH): | Diffusion processes, Bayesian statistical decision theory | ||||
Series Name: | Working papers | ||||
Publisher: | University of Warwick. Centre for Research in Statistical Methodology | ||||
Place of Publication: | Coventry | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.2009 | ||||
Number: | No.29 | ||||
Number of Pages: | 48 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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