Bernoulli

  • Bernoulli
  • Volume 12, Number 5 (2006), 863-888.

Convergence rates of posterior distributions for Brownian semimartingale models

F.H. Van Der Meulen, Aad W. Van Der Vaart, and J.H. Van Zanten

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Abstract

We consider the asymptotic behaviour of posterior distributions based on continuous observations from a Brownian semimartingale model. We present a general result that bounds the posterior rate of convergence in terms of the complexity of the model and the amount of prior mass given to balls centred around the true parameter. This result is illustrated for three special cases of the model: the Gaussian white-noise model, the perturbed dynamical system and the ergodic diffusion model. Some examples for specific priors are discussed as well.

Article information

Source
Bernoulli Volume 12, Number 5 (2006), 863-888.

Dates
First available in Project Euclid: 23 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1161614950

Digital Object Identifier
doi:10.3150/bj/1161614950

Mathematical Reviews number (MathSciNet)
MR2265666

Zentralblatt MATH identifier
1142.62057

Keywords
Bayesian estimation continuous semimartingale Dirichlet process Hellinger distance infinite-dimensional model rate of convergence wavelets

Citation

Van Der Meulen, F.H.; Van Der Vaart, Aad W.; Van Zanten, J.H. Convergence rates of posterior distributions for Brownian semimartingale models. Bernoulli 12 (2006), no. 5, 863--888. doi:10.3150/bj/1161614950. https://projecteuclid.org/euclid.bj/1161614950.


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