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Gao, Chao; Zhou, Harrison H.

Rate exact Bayesian adaptation with modified block priors. (English) Zbl 1331.62215

Ann. Stat. 44, No. 1, 318-345 (2016).
Summary: A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rate-optimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequence model, Gaussian regression and spectral density estimation.

Cited in 9 Documents

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

Bayesian nonparametrics; adaptive estimation; block prior
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\textit{C. Gao} and \textit{H. H. Zhou}, Ann. Stat. 44, No. 1, 318--345 (2016; Zbl 1331.62215)
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