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Activity Number:
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665
- Regression Methods for Longitudinal Data
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Type:
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Contributed
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Date/Time:
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Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #305140
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Presentation
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Title:
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Posterior Contraction and Credible Sets for Filaments of Regression Functions
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Author(s):
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Wei Li* and Subhashis Ghosal
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Companies:
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Syracuse University and North Carolina State University
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Keywords:
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Bayesian nonparametrics;
nonparametric regression;
credible sets;
coverage;
filaments;
asymptotic theory
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Abstract:
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A filament consists of local maximizers of a smooth function when moving in a certain direction. Filamentary structures are important features of the shape of objects and considered as a useful lower dimensional characterization of multivariate data. There have been some recent theoretical studies of filaments in the nonparametric kernel density estimation context. We shall discuss a Bayesian approach to the filament estimation in regression context and present some results on posterior contraction rates obtained using a finite random B-splines series. Compared with the kernel-estimation method, the bias can be better controlled using the series method when the function is smoother, which allows obtaining better rates. In addition, we discuss a way to construct a credible set with sufficient frequentist coverage for the filaments and demonstrate the proposed method in simulations and one application to earthquake data.
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Authors who are presenting talks have a * after their name.
