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October 2006 Convergence rates of posterior distributions for Brownian semimartingale models
F.H. Van Der Meulen, Aad W. Van Der Vaart, J.H. Van Zanten
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Bernoulli 12(5): 863-888 (October 2006). DOI: 10.3150/bj/1161614950

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.

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F.H. Van Der Meulen. Aad W. Van Der Vaart. J.H. Van Zanten. "Convergence rates of posterior distributions for Brownian semimartingale models." Bernoulli 12 (5) 863 - 888, October 2006. https://doi.org/10.3150/bj/1161614950

Information

Published: October 2006
First available in Project Euclid: 23 October 2006

zbMATH: 1142.62057
MathSciNet: MR2265666
Digital Object Identifier: 10.3150/bj/1161614950

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

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

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Vol.12 • No. 5 • October 2006
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