Non parametric Bayesian drift estimation for one-dimensional diffusion processes
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...
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)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics
Faculty of Science > Statistics
|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|
|Number of Pages:||48|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
 G.O. Roberts A. Beskos, O. Papaspiliopoulos. Retrospective exact simulation of
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