Convergence rates of posterior distributions for Brownian semimartingale models

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

doi:10.3150/bj/1161614950

Convergence rates of posterior distributions for Brownian semimartingale models

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

Research output: Contribution to journal › Article › Scientific › peer-review

22 Citations (Scopus)

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.

Original language	English
Pages (from-to)	863-888
Number of pages	26
Journal	Bernoulli
Volume	12
Issue number	5
DOIs	https://doi.org/10.3150/bj/1161614950
Publication status	Published - 1 Jan 2006
Externally published	Yes

Keywords

Bayesian estimation
Continuous semimartingale
Dirichlet process
Hellinger distance
Infinite-dimensional model
Rate of convergence
Wavelets

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AB - 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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KW - Continuous semimartingale

KW - Dirichlet process

KW - Hellinger distance

KW - Infinite-dimensional model

KW - Rate of convergence

KW - Wavelets

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Convergence rates of posterior distributions for Brownian semimartingale models

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Keywords

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