Activity Number:
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166
- SPEED: Topics in Bayesian Analysis
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Type:
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Contributed
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Date/Time:
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Monday, July 30, 2018 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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Abstract #328564
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Presentation
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Title:
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A Theoretical Framework for Bayesian Nonparametric Regression: Orthonormal Random Series and Rates of Contraction
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Author(s):
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Fangzheng Xie* and Wei Jin and Yanxun Xu
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Companies:
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Johns Hopkins University and Johns Hopkins University and Johns Hopkins University
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Keywords:
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Bayesian nonparametric regression;
integrated L2-distance;
orthonormal random series;
rate of contraction
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Abstract:
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We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated L2-distance without assuming the regression function space to be uniformly bounded. The framework is built upon orthonormal random series in a flexible manner. A general theorem for deriving rates of contraction for Bayesian nonparametric regression is provided under the proposed framework. As specific applications, we obtain the near-parametric rate of contraction for the squared-exponential Gaussian process when the true function is analytic, the adaptive rates of contraction for the sieve prior, and the adaptive-and-exact rates of contraction for the un-modified block prior when the true function is alpha-smooth. Extensions to wavelet series priors and fixed-design regression problems are also discussed.
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Authors who are presenting talks have a * after their name.