F.H. van der Meulen
A.W. van der Vaart
J.H. van Zanten
- Convergence rates of posterior distributions for Brownian semimartingale models
- Volume | Issue number
- 12 | 5
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
Key words and Phrases: Bayesian estimation, Continuous
semimartingale, Dirichlet process, Hellinger distance, Infinite dimensional
model, Rate of convergence, Wavelets.
We consider the asymptotic behavior 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 centered 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.
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