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Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs

  • Pokern, Y.
  • Stuart, A.M.
  • van Zanten, J.H.
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001779
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 603-628

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:603-628
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    1. Harry Van Zanten, 2003. "On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 6(2), pages 199-213, May.
    2. Omiros Papaspiliopoulos & Yvo Pokern & Gareth O. Roberts & Andrew M. Stuart, 2012. "Nonparametric estimation of diffusions: a differential equations approach," Biometrika, Biometrika Trust, vol. 99(3), pages 511-531.
    3. Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
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