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van der Meulen, F. H.; van der Vaart, A. W.; van Zanten, J. H.

Convergence rates of posterior distributions for Brownian semimartingale models. (English) Zbl 1142.62057

Bernoulli 12, No. 5, 863-888 (2006).
Summary: 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.

Cited in 15 Documents

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
60J65 Brownian motion
62F15 Bayesian inference
60J60 Diffusion processes
62E20 Asymptotic distribution theory in statistics

Keywords:

Bayesian estimation; continuous semimartingales; Dirichlet processes; Hellinger distance; infinite-dimensional model; rate of convergence; wavelets
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References:

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